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Colour measurement
and mixture

/illiam de Wiveleslie Abney, Society for Promoting
Christian Knowledge (Great Britain). General ...

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THE ROMANCE OF SCIENCE.

COLOUR MEASUREMENT

AND

MIXTURE.

8Kit^ |iumix0U8 |Un8ir»(ion8.

CAPTAIN W. DE W. ABNEY, c.b.,r.e.,d.c.l.,f.r.s.

PUBLISHED UNDER THE DIRECTION OP THE COMMITTEE

OF GENERAL LITERATURE AND EDUCATION APPOINTED BY THE

SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.

LONDON: NORTHUMBERLAND AVENUE, W.C. ,*
43, QUEEN VICTORIA STREET. B.C.

BRIGHTON: 135, north street.
NEW YORK: E. & J. B. YOU NO & ca

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PREFACE.

Some ten years ago there were three measure-
ments of the spectrum which I set myself to carry
out ; the last two, at all events,: involving new
methods of experimenting. The three measure-
ments were : (ist) The heating effect ; (2nd) the
luminosity ; and (3rd) the chemical effect on vari-
ous salts, of the different rays of the spectrum.
The task is now completed, and it was in carrying
out the second part of it that General Festing, who
joined me in the research, and myself were led
into a wider study of colour than at first intended,
as the apparatus we devised enabled us to carry
out experiments which, whilst difficult under or-
dinary circumstances, became easy to make. On
two occasions, at the invitation of the Society of

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vi PREFACE.

Arts, I have delivered a short course of lectures on
the subject of Colour, and naturally I chose to
treat it from the point of view, of our own methods
of experimenting ; and these lectures, expanded and
modified, form the basis of the present volume.

As a treatise it must necessarily be incomplete,
as it scarcely touches on the history of the subject
— a part which must always be of deep interest.
The solely physiological aspect of colour has also
been scarcely dealt with ; that part which the
physicist can submit to measurement being that
which alone was practicable under the circum-
stances.

W. DE W. Abney.

South JCensingtoHf
istMay^ 1891.

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CONTENTS.

CHAPTER I.

Sources of Light — Reflected Light — Reflection from Roughened
Surfaces— Colour Constants . . , . , /. ii

CHAPTER IL

A Standard of Light — Formation of the Spectrum by Prisms and by
the Diffraction Grating — Wave-lengths of the principal Fraun-
hofer Line — Position of Colours in 3ie Spectrum . /. 17

CHAPTER in.

The Visible and Invisible Parts of the Spectrum— Methods for
showing the Existence of the Invisible Portions — Phosphores-
cence — Photography of the Dark Rays — Thermo-Electric
Currents /• 30

CHAPTER IV.

Description of Colour Patch Apparatus — Rotating Sectors — Method
of making a Scale for the Spectrum . . . . /. 41

CHAPTER y.

Absorption of the Spectrum— Analysis of Colour — Vibrations of ,
Rays — Absorption by Pigments— Phosphorescence— Interference

/. 51

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Vlil CONTENTS. .

CHAPTER VJ.

Scattered Light — Sunset Colours— Law of the Scattering by Fine
Particle^ — Sunset Clouds — Luminosities of Sunlight at different
Altitudes of the Sun , p. 62

\)Lamin(

CHAPTER VIL

losity of the Spectrum to Normal-eyed and Colour-blind
Persons — Method of determining the Luminosity of Pigments —
Addition of one Luminosity to another • • • /• 7^

CHAPTER VIII.

V Methods of Measuring the Intensity of the Different Colours of the
Spectrum, reflected from Pigmented Surfaces— Templates for
the Spectrum /. 88

CHAPTER IX.

Colour Mixtures— Yellow Spot in the Eye— Comparison of Different
Lights — Simple Colours by Mixing Simple Colours — Yellow and
Blue from White p, 112

CHAPTER X.

Extinction of Colour by White Lightc— Extinction of White Light
by Colour /. 126

CHAPTER XL

Primary Colours — Molecular Swings— Colour Sensations— Sensa-
tions absent in the Colour-blind ..../. 133

, CHAPTER XII.

ormation of Colour Equations — Koenig*s Curves — Maxwell's Ap-
paratus and Curves p, 147

CHAPTER XIIL

Match of Compound Colours with Simple Colours — ^All Colours
reduced to Numbers — Method of Matching a Colour with a
Spectrum Colour and White Light ...,/. 156

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CONTENTS. ix

CHAPTER XIV.

Complementaiy Colours— Complementary Pigment Colours— Mea-
surement of Complementary Colours • • . /. 167

CHAPTER XV.
Persbtence of Images on the Retina— The Use of Coloured Discs

A 179

CHAPTER XVI.

Contrast Colours— Measurement of Contrast Colours— Fatigue of
the Eye— After-Images . . . . . . /. 196

LIST OF ILLUSTRATIONS.

FI& PAGB

Colour-patch apparatus Frontispiece

1. Spectrum of sunlight 18

2. Carbon poles of an electric light 20

3. Curve for converting prismatic spectrum into wave-lengths 28

4. The thermopile 36

5. Heating effect of different sources of radiation 38

6. Colour-patch apparatus 42

7. Rotating sectors 46

5. Spectrum of Carbon Sodium and Lithium 48

9, Interference bands 60

10. Absorption of rays by the atmosphere 68

11. Luminosity curve of spectrum of the positive pole of the

electric light 78

12. Rectangles of white and vermilion 82

13. Arrangement for measuring the luminosities of pigments 83

14. Measurement of the intensity of rays reflected from white

and coloured surfaces 89

15. Intensity of rays reflected from vermilion, emerald green,

and French ultramarine 9^

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LIST OF ILLUSTRATIONS.

PAGE
97

99
loo

lOI

i6. Method of obtaining two patches of identical colour

17. Absorption by red, blue, and green glasses

18. Light reflected from metallic surfaces

19. Intensities of vermilion, carmine, mercuric iodide, and

Indian red

20. Intensities of gamboge, Indian yellow, cadmium yellow,

and yellow ochre 102

21. Intensities of emerald green, chromous oxide, and terre

verte 103

22. Intensities of indigo, Antwerp blue, cobalt, and French

ultramarine 104

23. Method of obtaining a colour template 105

24. Template of carmine 106

25. Template of luminosity of white l^bt 108

26. Absorption of transmitted and reflected light by Prussian

blue and carmine ... 107

27. Collimator for comparing the intensity of two sources of

light 109

28. Spectrum intensities of sunlight, gaslight, and blue sky ... no

29. Comparison of sun and sky lights Ill

30. Slide with slits to be used in the spectrum 113

31. Screen on which to match gamboge 116

32. Diaphragm in front of prism 128

33. Curve oisensitiveness of silver bromo-iodide 136

34. Curves of colour sensations 139

35. Koenig's curves of colour sensations 151

36. Maxwell's colour-box 152

37. Maxwell's curves of colour sensations 154

38. Chromatic circle 169

39. Disc to cause alternate opening and closing of two slits ... 180

40. Disc painted blue and red 181

41. Electro-motor with discs attached 182

42. Method of cutting disc to allow an overlap of a second disc 184

43. Arrangement to nnd value of gamboge in terms of emerald

green and vermilion 188

44. Disc arranged to give approximately all the spectrum

colours 192

45. Method of showing contrast colours 196

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COLOUR MEASUREMENT

AND

MIXTURE.

CHAPTER I.

Sources of Light — Reflected Light — Reflection from
Roughened Surfaces — Colour Constants.

There is nothing, perhaps, in our everyday life
which appeals more to the mind than colour, yet
so accustomed are the generality of mankind to
i',s influence that but few stop to inquire the " why
and wherefore " of its existence, or its cause. To
those few, however, there is a source of endless
and boundless enjoyment in its study ; for in the
realms of physical and physiological science there
is perhaps no other subject in which experiments
give results so fascinating and often so beautiful.
Although its serious study must be undertaken
with a clear mind, a good eye, and a fair supply

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12 COLOUR MEASUREMENT AND MIXTURE.

of patience, yet a general idea of the subject may
be grasped by those who are possessed of but
ordinary intelligence.

Colour phenomena are encountered nearly every
day of one's life, and the fact that they are so
frequently met with, prevents that attention to
them, or even their remark. Who amongst us, for
instance, has noticed the existence of what are
called positive and negative after images, after
looking at some strongly illuminated object, or
would have gauged the fact that a certain portion
of the nervous system can be fatigued by a colour,
and give rise to images of its complementary, had
not an enterprising advertiser, who manufactures
a household necessary, drawn attention to it in a
manner that could not be misunderstood.

If on an autumn afternoon we pass through a
garden • whilst it is still perfectly light, we can
notice the gorgeous colouring of the flowers, and
appreciate with the eyes the beauty of each tint.
As evening comes on the tints darken, the darkest-
coloured flowers begin to lose their colour, and
only the brightest strike the eye. When night
still further closes in every colour goes, though the
outlines of the flowers may still be distinguished ;
and it would not be impossible, in some parts, to
see a tiny speck of pale light upon the ground
amongst them. This speck of light we should know

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COLOUR MEASUREMENT AND MIXTURE. 1 3

from experience to be the light from a glow-worm.
Why is it that we lose the colour of the flowers
and rec(^rnize the tiny light from this small worm ?
The reason for the one is that in order for objects,
which are not self-luminous to be seen at all, light
must fall on them and illuminate them, and the
light which they reflect may be coloured if they
po ssess t he^ualit ies toj reflect coloured light. The
glow-worm's light is seen, not because it"3bes not
emit light in the day-time, but because the eye,
being limited in sensitiveness, is unable to dis-
tinguish it when it is flooded with the light of day.
The glow-worm, however, is self-luminous, as is
shown by the fact that it emits light in the dark,
the light itself being slightly coloured if compared
with that of day. That a candle-flame or the sun
is self-iuminous is an axiom, and need not be
philosophised upon ; but what must be impressed
on the reader is, that though ajLjobject^which
requites to be illuniinated to be seen, is not self-
luminous, yet when illuminated it does in fact
become a source of illumination to the eye, although
the light IS only light reflected from its surface. It
is a point worth remembering that the rougher the
surface of an object, the brighter to the eye it will
b^ That iSjli coloured object when polished will
be a bad secondary source of illumination, as the
light incident upon it will be very nearly reflected

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14 COLOUR MEASUREMENT AND MIXTURE.

from the surface, according to the ordinary laws of
reflection ; but if it be roughened it will become
a much better source, as the roughnesses, though
obeying the laws of reflection, will reflect light in
every direction. A good example of this is an
ordinary sheet of glass. Light from a source falling
on its surface is scarcely reflected in any direction
except in that determined by the ordinary laws of
reflection, and it will be scarcely visible to the eye.
Grind its surface, however, and the innumerable
facets caused by the grinding will reflect light back
to the eye in whatever position it be placed, and
will thus be distinctly seen.

We may here premise that even the roughest
surface will reflect a greater percentage — varying
greatly according to the nature of the surface — of
light in the direction which it would do if it were
a smooth surface than in any other ; and in taking
measurements of the light irregularly reflected
from a rough surface, this fact must be borne in
mind.

Not only must we know how colour is produced,
but we must also be able to refer it to some
standard which shall be readily reproduced, and
which shall be unalterable. There are two variable
factors which have to be taken into account in
colour experiments : the ^rst is the quality of
light which illuminates the obje ct, and the second

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COLOUR MEASUREMENT AND MIXTURE. IS

is the sensitiveness of the eye which perceives i t.
as light is only a sensation which is recognized by
the brain through the medium of the eye. We
shall, as we go on, see that different qualities of
light may cause objects to appear of different
hues, and further that eyes may vary in perceptive
power, to an extent of which the large majority of
people are not aware^ Hence it becomes necessary
as far as possible to eliminate these variables.
^ The task which we have set ourselves to perform
then, is first to find a suitable light for experi-
mental work, and next to endeavour to refer colour
to an eye which has no abnormal defects. This
being accomplished, we have then to find means to
measure the different constants which are involved
in colour, and to refer the measurements to some
standard. Col our q gpgt jints are three, viz. hue,
luijiinosity, ai^g^urity; and it will be seen that
if these three are determined, the measurement of
the colour is complete.

Perhaps the meaning of these terms may require
to be explained. The hue of a colour is what in
common parlance is often called the colour. Thus
we talk of rose, violet, magenta, emerald green, and
so on, but for measuring purposes the hue had best
be referred to the spectrum colours as a standard
(the means of doing so will be shortly explained),
for they are simple colours, which can be expressed

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l6 COLOUR MEASUREMENT AND MIXTURE.

by numbers. Compound colours, which it may be
said are invariably to be found in nature, being
mixtures of simple colours, can be just as readily
referred to the spectrum./ By thejunijnosity of_a
colour we mean its brightness, the standard of refer-
ence being the brightness of a white surface when
illuminated by the same white light By the £urity
of a colour we mean its freedom from admixture
with white light. An example of different degree
of purity will be found in washes of water-colours
of different tenuity. Thus if we wash a sheet of
paper with a light tint of carmine, the whiteness
of the paper is not obliterated ; if we pass another
wash over it the whiteness of the paper is lessened,
and so on. The lightest tint is that which is nK>st
lacking in purity.

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CHAPTER IL

A Standard Light — Formation of the Spectrum by Prisms
and by the Diffraction Grating — Wave-lengths of the
principal Fraunhofer Line — Position of Colours in the
Spectrum.

As we have to turn to the spectrum- for pure and
simple colours, from which we may produce any-
compound colour we may wish to deal with, we
will first consider the light with which we shall
form it A spectrum may be produced from any
source of light, such as sunlight, limelight, the
electric light, gaslight, or incandescence electric
light, as also from incandescent vapours, or gases ;
but it is only a solid which is, or is rendered incan-
descent, that will give us a continuous spectrum, as
it is called, that is, a spectrum which is unbroken
by _gags of non-luminosity, or sudden change of
brightness, throughout its length.

The great desideratum for the study of colour
is a light which not only gives a practically

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l8 COLOUR MEASUREMENT AND MIXTURE.

continuous spectrum, but one which is produced by
the radiation of matter which is black when cold,
and which can be kept at a con-
stantly high temperature. We
have purposely said " black " in
the sentence above, since it is
believed that differently coloured
bodies, when heated to equal
temperatures, might not give the
same relative intensities to the
different parts of the spectrum, ^^^^HH l*
the variation being dependent on ^^^^^^H d
the colour of the heated body. ^^^^^B s
A black body must always give ^^^^^^ -
the same visible spectrum when ^^^^^H J*
heated to the same temperature.
The spectrum of sunlight (Fig. ^^^^^^| s
i) is not continuous, as we find ^^^^^^" ^
it crossed by an innumerable
number of fine lines of varying
breadth and blackness. This
want of continuity would not
be fatal to its adoption were
it possible to use it outside
the limits of our atmosphere,
as then, unless the temperature of the sun itself
changed, the spectrum produced would be invari-
able ; but unfortunately the relative brightness or

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COLOUR MEASUREMENT AND MIXTURE. I9

luminosity of the different parts of the spectrum
varies from day to day, and hour to hour, according
to the height of the sun above the horizon (see
Chap. VI.) ; and its integral brightness varies ac-
cording to the clearness of the sky. It is evident
then, that, as a reference light, sunlight is most
unsuitable, so we may dismiss it from our possible
standards.

By the process of elimination we may arrive at
the light upon which we can rely, for the purpose
we have in view, viz. the production of a spec-
trum of moderate size, and sufficiently bright to
be well viewed when projected upon a screen.
For some purposes, as for instance in becoming
acquainted with the general character of the
spectrum, a feebler light, such as gaslight, or light
from electrical glow lamps, may be employed, since
the spectrum may be viewed directly by the eye
without the intervention of a screen. They have
two drawbacks for our object : one being the want
of general intensity, and the other the feeble
luminosity of blue and violet rays in their spec-
trum (see page ijo). The limelight we can also
dismiss for want of steadiness. Its whiteness and
luminosity varies according to the oxygen playing
on the lime cylinder, rendering the relative inten-
sities of the different parts of the spectrum so
erratic as to make it unreliable. This leaves the

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20 COLOUR MEASUREMENT AND MIXTURE.

(electric) arc-light as the only one which is really
available. Remember how the arc-light is pro-
duced. A current of electricity passes between
the ends of two thick black carbon rods, or poles
as they are called, through an air space of small
interval, and the passage of the current renders the
tips of these rods white-hot (Fig. 2). The centre of
the end of one pole, called the
positive pole, where a crater-like
depression is formed, is the
part which attains the whitest
heat, and its temperature seems
to be constant, and to be that
of the volatilization of carbon.
Numerous experiments have
been made by the writer, and
he has found that the light
emitted by this crater in the
positive pole is, within the

limits of the error of observ- Fig. a^The Carbon Poles

ation, always of the same white- ^^^ ^^^^ ^«^^-. ^
ness, and consequently gives a spectrum which is
unvarying in the proportionate intensities of the
different colours. When the experiments made to
determine the luminosity of the spectrum are de-
scribed, the method of ascertaining this will be
readily understood.

In the spectrum produced by this light there are

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COLOUR MEASUREMENT AND MIXTURE. 21

two places in the violet where there are bands of
violet lines slightly brighter than the general spec-
trum. They are principally due to the light emitted
from the incandescent vapour of carbon, which is
volatilized and plays between the two poles (see
Fig. 2) ; but as these bands are of but small
visual intensity, and situated towards the limit of
the visible spectrum, they do not interfere with
eye-measures of colours, though they do, to a
certain extent, to the analysis of radiation by
photography. If we throw the positive pole a
little behind the negative pole we can, however,
considerably mitigate this evil. We can separate
the carbon rods to such a degree that the white-
hot crater faces the observer, and a good deal of
the arc is hidden. This is well seen in the figure.

We have now described the light we have
adopted, and the reasons for adopting it; and
having obtained our light, we can now consider by
what plan we shall form our spectrum. There are
two ways open to us — one by glass prisms, and
the other by a diffraction grating. Glass prisms
separate white light, or indeed any light, into its
components, from the fact that the refraction of
each coloured ray differs from every other. Thus
the red rays are least refracted, and the violet the
most, and the yellow, green and blue are inter-
mediate between them, being placed in the order

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22 COLOUR MEASUREMENT AND MIXTURE.

of least refrangibility. Between these there is of
course every shade of simple colour, one melting
into the other. In order to form a pure and
bright spectrum with prisms, in a room of limited
dimensions, we have to use certain auxiliary ap-
paratus which are not positively essential, though
convenient. C^he real essentials to form a spectrum
are a narrow slit, a glass prism, with perfectly plane
faces, and a lens. If this be the only apparatus
available, the slit must be placed at a long distance
from the prism, the beam of light must pass through
the slit on to the prism, and the lens must be placed
at such a distance from the slit that it forms a sharp
image on a screen. When the light passes through
the prism, the screen will have to be rotated in the
arc of a circle, so that its distance from the slit
measured along the line of the ray to the prism,
and from the prism to the screen, is the same as it
would be without the intervening prism. An ap-
paratus of this description is not convenient, how-
ever, as it requires much more space than is often
available. If a lens be placed between the slit
and the prism, at exactly its focal length from the
former, the light entering the slit will, after passage
through the lens, emerge as parallel rays, that is,
they will emerge as they would do if th^ slit were
placed at an infinite distance from the observer.
The focal length of this coUimating lens need

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COLOUR MEASUREMENT AND MIXTURE. 23

not be greater than twelve to eighteen inches, so
that the gp'eat space required by the cruder
apparatus is very much curtailed. The lens and
slit are mounted one at each end of a tube of the
necessary length, and are thus handy to use.

Instead of one prism two or three may be used,
giving an angular dispersion of the spectrum two
or three times respectively greater than that which
would be given by only one prism ; consequently
td obtain a given length of spectrum with the in-
creased dispersion, the focal length of the lens used
to focus the image on the screen may be diminished.

The drawback to the use of prisms is that the
dispersion of the red end of the spectrum is much
less than that of the blue end, and is apt to give a
false impression as to the relative luminosities of,
and length of spectrum occupied by, the different
colours. In some te«t-books it is told us that the
diffraction grating gives us a dispersion which is in
exact relation to the wave-length. This is not true,
however, as it can only give one small portion in
such relationship, and that only when it is specially
set for the purpose. The subject of diffraction is
one into which it would be foreign to our purpose
to wander. We may say that for measures such as
we shall make, it is handier to employ prisms, as
the prismatic spectrum is more intense than the dif-
fraction spectrum. This can be readily understood

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24 COLOUR MEASUREMENT AND MIXTURE.

when we consider the subject even superficially.
If we throw a beam of light on a grating which
contains perhaps some 14,000 parallel lines in the
space of one inch in width, the lines being ruled on
a plane and bright metallic surface, and receive the
reflected beam on a screen, the appearance that is
presented is a white central spot, together with six
or seven spectra of gradually diminishing bright-
ness on each side of it, all except the first pair
overlapping one another. That these different
spectra do exist can be readily shown by placing
in the beam a piece of red glass, when symmetri-
cal pairs of the red part of the spectrum will
be found, one of each pair being on opposite sides
of what will now be the central red spot. Half
the light falling on the grating is concentrated in
this central spot, and the remaining half goes to
form the spectra ; the pair nearest the central spot
being the brightest. We thus are drawn to the
conclusion that at the outside we can only have
less than one-quarter of the incident light to form
the brightest spectrum we can use. With two good
prisms we use at last three-fourths of the incident
light, so that for the same length of spectrum we
can get at least three times the average brightness
that we should get were we to employ a diffraction
grating.

We must now refresh the reader's memory with

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COLOUR MEASUREMENT AND MIXTURE. 2$

a few simple facts about light, in order that our
meaning may be clear when we speak of rays of
different wave-lengths. Every colour in the spec-
trum has a different wave-length, and it is owing
to this difference in wave-length that we are able
to separate them by refraction, or diffraction, and
to isolate them. Light, or indeed any radiation, is
caused by a rhythmic oscillation of the impalpable
medium which we, for want of a better term, call
ether, and the distance between two of these waves
which are in the same phase is called the wave-
length of the particular radiation. The extent of
the oscillation is called the amplitude, which when
squared is in effect a measure of the intensity of
the radiation. Thus at sea the distance between
the crests of two waves is the wave-length, and the
height from trough to crest the amplitude ; and the
intensity, or power of doing work, of two waves
of the same wave-lengths but of different heights,
is as the square of their heights. Thus, if the
height of one were one unit, and of the other two
units, the latter could do four times more work than
the former. The waves of radiation which give the
sensation of colour in the spectrum vary in length,
not perhaps to the extent that might be imagined,
considering the great difference that is perceived
by the eye, but still they are markedly different.
The fact that the spectrum of sunlig^stP^H
tinuous,but is broken up by innura^atje J^l

^ / frr' *■-* *»»**' C '. "^ *^\

26 COLOUR MEASUREMENT AND MIXTURE.

has already been alluded to. The position of these
lines is always the same, as regards the colour in
which they are situated, and is absolutely fixed
directly we know their wave-length ; hence if we
know the wave-lengths of these lines, we can refer
the colour in which they lie to them. Now some
lines of the solar- spectrum are blacker and con-
sequently more marked than others, and instead of
referring the colours to the finer lines, we can refer
them to the distance they are from one or more of
these darker lines, where these latter are absolutely
fixed ; in fact they act as mile-stones on a road.

In the red we have three lines in the solar spec-
trum, which for sake of easy reference are called A,
B and C ; in the orange we have a line called D,in
the green a line called E, in the blue F, in the violet
G, and in the extreme violet H. These lines are
our fiducial lines, and all colours can be referred to
them. The following are the wave-lengths of these
lines, on the scale of ^^—^ of a millimetre as a unit

A ...' ... 7594
B •.. ..• ^6f
C ... ... 6562

D 5892

E 5269

F 4861

G 4307

H 3968

When the spectrum is produced by prisms the
intervals between these lines are not proportional

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COLOUR MEASUREMENT AND MIXTURE. 2^

to the wave-lengths, and consequently if we measure
the distance of a ray in the spectrum from two of
these lines, we have to resort to calculation, or to
a graphically drawn curve, to ascertain its wave-
length. For the purpose of experiments in colour
the graphic curve from which the wave-length can
immediately be read off is sufficient. The following
diagram (Fig. 3) shows how this can be done.

The names and range of the principal colours
which are seen in the spectrum has been a matter
of some controversy. Professor Rood has, however,
made observations which may be accepted as cor-
rect with a moderately bright spectrum. If the
spectrum be divided into 1000 parts between A in
the red, and H, the limit of the violet, he makes
the following table of colours.

Scale.

Colour.

149

Red.

149 to

194

Orange red.

194 to

210

Orange.

210 to

230

Orange yellow.

230 to

240

Yellow.

240 to

344

Yellow green and
green yellow.

344 to

447

Green and blue
green.

447 to

495

Azure blue.

495 to

806

Blue and blue violet

806 to

1000

Violet

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 29

In the above scale (Fig. 3) A « o, B = 74*0, C =
1 127, D = 220-3, E = 3631, F = 493-2, G = 753-6,
H= 1000.

These are the main subdivisions of colour, but it
must be recollected that one melts into the other.
When the spectrum is very bright the colours
tend to alter in hue ; thus the orange becomes
paler, and the yellow whiter, and the blue paler.
On the other hand, if the spectrum be diminished
in brightness the tendency is for the colours to
change in the opposite direction. Thus the yellow
almost disappears and becomes of a green hue,
whilst the orange becomes redder, and the spectrum
itself becomes shorter to the eye than before.

Let us strictly guard ourselves, however, from
the criticism that all eyes see not alike. Suffice
it to say that the above table is correct for the
ordinary or normal eye, and does not necessarily
apply to those who have defective vision as regards
colour sensation.

dbyGoogk

CHAPTER III.

The Visible and Invisible Parts of the Spectrum— Methods
for showing the Existence of the Invisible Portions-
Phosphorescence — Photography of the Dark Rays —
Thermo-Electric Currents.

We are apt to forget, when looking at the spec-
trum, that what the eye sees is not all that is to
be found in the prismatic analysis of light The
spectrum, it must be recollected, is not limited to
those rays which the eye perceives. There are ra)^
both beyond the extreme violet and below the ex-
treme red, which exist and which- exercise a marked
effect on the world's economy. Thus, rays beyond
the violet are those which with the violet and the
blue rays principally affect vegetation, enabling
certain chemical changes to take place which are
necessary for its growth and health; whilst the
rays below the red are those possessing the
greatest amount of energy, and if they fall upon
bodies which absorb them, as very nearly all

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COLOUR MEASUREMENT AND MIXTURE. 3 1

bodies do to a certain extent, they heat them.
The warmth we feel from sunlight is principally
due to the dark rays which lie below the red of
the spectrum.

The existence of both kinds of these dark rays
may be demonstrated in a very simple manner
by the effect that they produce on certain bodies.
For instance, there is a yellow dye with which
cheap ribbon is dyed, which if placed in the
spectrum and beyond the violet causes a visible
prolongation of the spectrum. The light in the
newly-seen and once invisible part of the spectrum
is yellow, the colour of the ribbon itself. In fact,
the whole of that part of the spectrum, which on
the white screen is seen as blue and violet, becomes
yellow, the red and green remaining unchanged.
This change in colour is due to fluorescence, a
phenomenon of light which Sir G. Stokes found
was caused by an alteration in the lengths of the
waves of light when reflected from certain bodies.
It is not meant to imply by this that the wave-
length of any ray falling on a body can be altered
by reflection, but only that the body itself on
which the rays fall emits rays of light which are
not of the same wave-length as those which fall
upon it Now it is a fact that the rays that He
beyond the violet, and which are ordinarily invisible,
are shorter than the violet rays, and that these are

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32 COLOUR MEASUREMENT AND MIXTURE.

shorter than the yellow rays. It follows therefore
that when, what we may now call, the ultra-violet
rays fall on the yellow dyed ribbon, the waves
emitted by it are so lengthened that they appear
yellow to the eye instead of dark, violet, or blue.

We can also brush a solution of quinine on the
scrieen, and immediately the place where the ultra-
violet rays fall is illuminated by a violet light. We
do not see the ultra-violet rays themselves, but only
the rays of increased wave-length, which are emitted
by their effect on the sulphate of quinine. Common
machine oil as used for engines also emits greenish
rays when excited by the ultra-violet rays, and a very
beautiful colour it is. Fluorescence then is one means
of demonstrating the existence of the ultra-violet
rays— or Ritter's rays as they were formerly called,
after their discoverer — in a very simple manner.
The method of rendering the effects of the infra-red
rays visible to the eye is also interesting. All, or at
all events most, of our readers have seen Balmain's
luminous paint. A glass or card coated with this
substance, which is essentially a sulphide of calcium,
when exposed to the light of the sun, or of the electric
arc, and then taken into comparative darkness, is
seen to shine with a peculiar, violet-coloured light
If when thus excited we place it in a bright spec-
trum for some little time, we shall find on shutting
off the light that where the ultra-violet and blue

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COLOUR MEASUREMENT AND MIXTURE. 33

fell on it, the violet light is intenser than the light
of the main part of the screen ; where the yellow
fell there is neither increase or diminution in bright-
ness ; but that in the red it becomes darker, and
also beyond the limit of the visible spectrum, indi-
cating the existence of rays beyond, which through
their greater length have not the power of affecting
the eye. If the spectrum be shut off, however, very
soon after it falls on the plate, it has been asserted
that the red and infra-red rays have increased the
brightness of that particular part of the plate on
which they fell. At first these two observations
seem to contradict one another; they do not in
reality. We may expose a tablet of Balmain's
paint to light, and place a heated iron in contact
with the back of the plate ; we shall then find that
the iron produces a bright image of its surface on
a less bright background. This bright image will
gradually fade away, and the same space will
eventually become dark compared with the rest
of the plate. The reason of this is clear. When
light excites the paint a certain amount of energy
is poured into it, which it radiates out slowly as
light When the hot iron is placed in contact with
it, the heat causes the light to radiate more rapidly,
and consequently with greater intensity, at the part
where its surface touches, and the energy of that

particular portion becomes used up. When the

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34 COLOUR MEASUREMENT AND MIXTURE.

energy of radiation of this part becomes less than
that of the rest of the tablet, its light must of
necessity be of less brightness than that of the
background, wijth which the heated iron has had
no contact. For this reason the image of the iron
subsequently appears dark. We shall see presently,
and as before stated, that the principal heating
effect of the spectrum lies in the red and infra-red,
and it is owing to the heating of the paint by these
rays that the image might be at first slightly brighter
than the background, and subsequently darker.

There is another way in which the existence of
both the ultra-violet and infra-red rays can be
demonstrated, and that is by means of photography.
If we place an ordinary photographic plate in
the spectrum and develop it, we shall find that
besides being affected by the blue and violet rays,
it is also affected by the rays beyond the violet,
the energy of these rays being capable of causing a
decompositioji of the sensitive silver salt. If quartz
prisms and lenses be used, and the electric light
be the source of illumination, the ultra-violet spec-
trum will extend to an enormous extent. A more
difficult, but perhaps even more interesting means
of illustrating the existence of the infra-red rays,
and first due to the writer, can be made by means
of photography. It is possible to prepare a photo-
graphic plate with bromide of silver, which is so

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COLOUR MEASUREMENT AND MIXTURE. 35

molecularly arranged that it becomes capable of
being decomposed not only by the violet and blue
rays, but also by the red rays, and by those rays
which have wave-lengths of nearly, three times that
of the red rays. It -would be inappropriate to
enter into a description of the method of the pre-
paration of these plates. Those who are curious
as to it will find a description in the Bakerian
lecture published in the Philosophical Transactions
of the Royal Society for 1881. With plates so
prepared it has been found possible to obtain im-
pressions in the dark with the rays coming from a
black object, heated to only a black heat.

That these dark rays possess greater energy or
capacity for doing work of some kind than any
other rays of the spectrum, can be shown by means
of a linear thermopile (Fig. 4), if it be so arranged
as to allow only a narrow vertical slice of light to
reach its face.

The principle of the thermopile we need not
describe in detail. Suffice it to say that the heat-
ing of the soldered junctions of two dissimilar
metals (there are ten pairs of antimony and bis-
muth in the above instrument) produces a feeble
current of electricity, which, however, is sufficient
to cause a deflection to the suspended needle of
a delicate galvanometer. To the needle is attached
a mirror weighing a fractioa of a grain, and the

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36 COLOUR MEASUREMENT AND MIXTURE.

deflections are made visible by the reflection from
it of a beam of light issuing from a fixed point
along a scale. The greater the heating of the

Fig. 4.— The Thermopile.

junctions of the thermopile, within limits which
in these cases are never exceeded, the greater
is the current produced, and consequently the

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COLOUR MEASUREMENT AND MIXTURE. 37

greater is the deflection of the mirror-bearing
needle, and of the beam of light along the scale.
In order to get a comparative measure of the
energies of the different rays, it is necessary that
they should be completely absorbed. Now the
junctions themselves of the pile being metal, and
therefore more or less bright, will not absorb com-
pletely, but if they be coated with a fine layer of
lamp-black, the rays falling on the pile will be
absorbed by this substance, and their absorption
will cause a rise in temperature in it, and the heat
will be communicated to the thermopile.

If we make a bright spectrum, and one not too
long, say three inches in length, and pass the linear
thermopile through its length, we shall find that
when the galvanometer is attached, the galvano-
meter needle will be differently deflected in its
various parts. The deflection will be almost insen-
sible in the violet, but sensible in the blue, rather
more in the green, still more in the yellow, and
it will further increase in the red. When, however,
the slit of the thermopile is placed beyond the limit
of the visible spectrum, the deflection enormously
increases, and will increase till a position is reached
as far below the red as the yellow is above it.
After this maximum is reached, by moving the
pile still further from the red, the galvanometer
needle will travel towards its zero, and finally

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38 COLOUR MEASUREMENt ANt) MIXTURE.

all deflection will cease. At this point we may sup-
pose we have reached the limit of the spectrum,
but if rock-salt prisms and lenses be used, the limit
will be increased. What the real limit of the
spectrum is, is at present unknown ; Mr. Langley

VIQLST BiilE a&£mQBmG£.&£P DARK

Fig. 5.— Heating effect of different Sources of Radiation.

with his bolometer, and rock-salt prisms, an instru-
ment more sensitive than the thermopile, must
have nearly reached it.

The above figure is a graphic representation
of the heating effect of the spectrum of the electric

dbyGoogk

COLOtJR MEASUREMENT AND MIXTURE. 39

light, sunlight, and the incandescence electric light,
on the lamp-black coating of the thermopile, as
shown by the galvanometer. The vast difference
between the heating effect of the visible rays of
the first two sources compared with the last is
clearly indicated.

Since every ray may be taken as totally ab-
sorbed, the heating of the lamp-black is a measure
of the energy or the capacity of performing work
of some description, which they possess. Waves
of the sea do work when they beat against the
shore, and they do work when they lift a vessel.
If we notice a ship at anchor we shall find that
behind the vessel and towards the shore the waves
are lowered in height or amplitude; the energy
which they have expended in raising the vessel of
necessity causes this lowering. In the same way
the waves of light, after falling on matter whose
molecules or atoms are swinging in unison with
them, are destroyed, and the energy is spent in
cither decomposing the matter into a simpler form
at first — though the subsequent form may be more
complex — or in raising its temperature. As lamp-
black or carbon is in its simplest form, the only
work done upon it by the energy of radiation is the
raising of its temperature, and it is for this reason
that this material is so excellent for covering the
junctions of the pile. The eye evidently does not

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40 (iOLOtJR MEASUREMENf ANt) MlXTURfi.

absorb all rays, since only a limited part of the
spectrum is visible, and it would be useless to
take a measure of the heating effect of lamp-black
for the visible part of the spectrum as a measure
of its luminosity, since the latter fades off in the
red — ^the very place in which the heat curve rises
rapidly.

dbyGoogk

CHAPTER IV.

Description of Colour Patch Apparatus— Rotating Sectors —
Method of making a Scale for the Spectrum.

Before proceeding further we must describe some-
what in detail two or three pieces of apparatus to
be used in the experiments we shall make.

The first piece was devised by the writer a few
years ago, and has got rid of several objections
which existed in older pieces of apparatus. It is
not only useful for lecture purposes, but also for
careful laboratory work. The ordinary lecture
apparatus for throwing a spectrum on the screen
is of too crude a form to be effective for the pur-
pose we have in view ; the purity of the colours
seen on the screen is more than doubtful, and this
alone unfits it for our experiments. If we want
to form a pure spectrum we must have a narrow
slit, prisms with true, flat surfaces, and lenses of
proper curvature. As a rule the ordinary lecture

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4^ COLOUk MEASUREMENt ANt) MIXtURfi.

apparatus for forming the spectrum lacks all of
these requisites

Fig. 6. — Colour Patch Apparatus.

The accompanying diagram (Fig. 6) will f^ve an
idea of the apparatus we shall employ. On the usual
slit Si of a collimator C is thrown, by means of a

dbyGoogk

COLOUR MfiASDRteMENt ANt) MlJCTURfi. 4^

condensing lens Li, a beam of light, which emanates
from the intensely white-hot carbon positive pole
of the electric light The focus is so adjusted
that an image of the crater is formed on the
slit The coUimating lens La is filled by this
beam, and the rays issue parallel to one another
and fall on the prisms Pj and P2, which disperse
them. The dispersed beam falls on a corrected
photographic lens L3, attached to a camera in the
ordinary way. It is of slightly larger diameter
than the height of the prisms, and a spectrum is
formed on the focussing-screen D, which is slewed
at a slight angle with the perpendicular to the axis
of the lens Lg. This is necessary, because the focus
of the least refrangible or red rays is longer than
that of the more refrangible or blue rays. By
slewing the focussing-screen as shown, a very good
general focus for every ray may be obtained. When
the focussing-screen is removed, the rays form a
confused patch of parti-coloured light on a white
screen F, placed some four feet off the camera.
The rays, however, can be collected by a lens L4,
of about two feet focus, placed near the position
of the focussing-screen, and slightly askew. This
forms an image on the screen of the near surface
of the last prism Pa ; and if correctly adjusted, the
rectangular patch of light should be pure and with-
out any fringes of colour. The card D slides into

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44 COLOUR MfiASUREMENt AND MIXTURE.

the grooves which ordinarily take the dark slide.
In it will be seen a slit Ss» the utility of which will
be explained later on.

We shall usually require a second patch of white
light, with which to compare the first patch. Now,
although the light from the positive pole of the
carbons is uniform in quality, it sometimes varies in
quantity, as it is difficult to keep its image always
in exactly the centre of the slit If we can take one
part of the light coming through the slit to form
the spectrum, and another part to form the second
patch of white light, then the brightness of the
two will vary together. At first sight this might
appear difficult to attain ; but advantage is taken
of the fact that from the first surface of the first
prism Pi a certain amount of light is reflected.
Placing a lens L5, and a mirror G, in the path of
this reflected beam, another square patch of light
can be thrown on the same screen as that on which
the first is thrown, and this second patch may be
made of the same size as the first patch, if the lens
L5 be of suitable focus, and it can be superposed
over the first patch if required ; or, as is useful in
some cases, the two patches may be placed side
by side, just touching each other.

We are thus able to secure two square white
patches upon the screen F, one from the re-combin-
ation of the spectrum, and one from the reflected

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COLOUR MEASUREMENT AND MIXTURE. 45

beam. If a rod be placed in the path of these
two beams when they are superposed, each beam
will throw a shadow of the rod upon the screen.
The shadow cast by the integrated spectrum will
be illuminated by the reflected beam, and the
shadow cast by the latter will be illuminated by
the former. In fact we have an ordinary Rumford
photometer, and the two shadows may be caused
to touch one another by moving the rod towards
or from the screen. When the illumination of the
two shadows by the white light is equal, the whole
should appear as one unbroken gray patch. To
prevent confusion to the eye a black mask is
placed on the screen F with a square aperture cut
out of it, on which the two shadows are caused to
fall. If it be desired to diminish the brightness of
either patch, it can be accomplished by the intro-
duction of rotating sectors M, which can be opened
and closed at pleasure during rotation, in the path
of one or other of the beams.

The annexed figure (Fig. 7) is a bird's-eye view of
the instrument. A A are two sectors, one of which
is capable of closing the open aperture by means
of a lever arrangement C, which moves a sleeve in
which is fixed a pin working in a screw groove,
which allows the aperture in the sectors to be
opened and closed at pleasure during their revo-
lution ; D is an electro-motor causing the sectors

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46 COLOUR MEASUREMENT AND MIXTURE.

to rotate. To show its efficiency, if two strips of
paper, one coated with lamp-black and the other
white, are placed side by side on the screen, and if
one shadow from the rod falls on the white strip,
and the other shadow on the black strip of paper,

Fig. 7. — Rotating Sectors.

and the rotating sectors are interposed in the path
of the light illuminating the shadow cast on the
white strip, the aperture of the sectors can be
closed till the white paper appears absolutely
blacker than the black paper. White thus be-
comes darker than lamp-black, owing to the want

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 47

of illumination. This is an interesting experiment,
and we shall see its bearings as we proceed, as it
indicates that even lamp-black reflects a certain
amount of white or other light.

Having thus explained the main part of the
apparatus with which we shall work, we can go on
and show how monochromatic light of any degree
of purity can be produced on the screen. If the
slit in the cardboard slide D be passed through
the spectrum when it has been focussed on the
focussing-screen, only one small strip of practically
monochromatic light will reach the screen, and
instead of the white patch on the screen we shall
have a succession of coloured patches, the colour
varying according to the position the slit occupies
in the spectrum. It should be noted that the
purity of the colour depends on two things — the
narrowness of the slit Si of the collimator, and of
the slit Sa in the card. If two slits be cut in the
card D, we shall have two coloured patches over-
lapping one another, and if the reflected beam
falls on the same space we shall have a mixture
of coloured light with white light, and either the
coloured light or the white light can be reduced
in brightness by the introduction of the rotating
sectors. If the rod be introduced in the path of
the rays we shall have two shadows cast, one illu-
minated with coloured light, monochromatic or

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48 COLOUR MEASUREMENT AND MIXTURE.

compound, and the other with white light, and
these can be placed side by side, and surrounded
by the black mask as before described.

There is one other part of the apparatus which
may be mentioned, and that
is the indicator, which tells
us what part of the spectrum
is passing through the slit.
Just outside the camera, and
in a line with the focussing-
screen, is a clip carrying a
vertical needle. A small beam
of light passes outside the
prism Pi; this is caught by
a mirror attached to the side
of the apparatus, and is re-
flected so as to cast a shadow
of the needle on to the back
of the card D, on which a
carefully divided scale of
twentieths of an. inch is
drawn. To fix the position
of the slit the poles of the
electric light are brushed over
with a solution of the carbon-
ates of sodium and lithium in
hydrochloric acid, and the image of the arc is
thrown on the slit. This gets rid of the continuous

dbyGoogk

COLOUR MEASUREMENT AND MIXtURE. 49

spectrum, and only the bright lines due to the in-
candescent vapours appear on the focussing-screen
(Fig. 8). Amongst other lines we have the red
and blue lines due to the vapour of lithium ; the
orange, yellow (D), and green lines of sodium,
together with the violet lines of calcium (these
last due to the impurities of the carbons forming
the poles). These lines are caused successively to
fall on the centre of the slit by moving the card
D, which for the nonce is covered with a piece of
ground glass, and the position of the shadow of the
needle-point on the scale is registered for each. A
further check can be made by taking a photograph
of these lines, or of the solar spectrum, and having
fixed accurately on the scale any one of these lines
already named, the position of the others on the
scale may be ascertained by measurement from
the photograph. Now the wave-lengths of these
bright lines have been most accurately ascer-
tained, in fact as accurately as the dark lines in
the solar spectrum. Thus the scale on the card
is a means of localizing the colour passing through
the slit or slits. Should more than one slit be used
in the spectrum the positions of each can be deter-
mined in exactly the same way. The most tedious
part of the whole experimental arrangement with
this apparatus is what may be called the scaling
of the spectrum.

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50 COLOUR MEASUREMENT AND MIXTURE.

A fairly large spectrum may be formed upon the
screen without altering any arrangement of the
apparatus, when it has been adjusted to form colour
patches. If a lens Le (see Fig. 6) of short focus
be placed in front of L4 (the big combining lens),
an enlarged spectrum will be thrown upon the screen
F, and if slits be placed in the spectrum the images
of their apertures are formed by the respective
coloured rays passing through them, so that the
colours which are combined in the patch can be
immediately seen.

dbyGoogk

CHAPTER V.

Absorption of the Spectrum — Analysis of Colour — ^Vibrations
of Rays — Absorption by Pigments — Phosphorescence-
Interference.

We must now briefly consider what is the origin,
or at all events the cause, of the colour which
we see in objects. It is not proposed to enter into
this by any means minutely, but only sufficiently
to enable us to understand the subject which is to
be brought before you. What for instance is the
cause of the colour of this green solution of
chlorophyll, which is an extract of cabbage leaves ?
If we place it in the front of the spectrum ap-
paratus and throw the spectrum on the screen, we
find that while there is a certain amount of blue
transmitted, the green is strong, and there are red
bands left, but a good deal of the spectrum is
totally absorbed. Forming a colour patch of this
absorption spectrum on the screen, we see that it
is the same colour as the chlorophyll solution, and

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52 COLOUR MEASUREMENT AND MIXTURE.

of this we can judge more accurately by using
the reflected beam, and placing the rod in position
to cast shadows. (The light of the reflected beam
is that of the light entering the slit.) The colour
then of the chlorophyll is due to the absence of
certain colours from the spectrum of white light
When white light passes through it, the material
absorbs, or filters out, some of the coloured rays,
and allows others to pass more or less unaffected,
and it is the recombination of these last which
makes up the colour of the chlorophyll We have
a green dye which to the eye is very similar in
colour to chlorophyll, but putting a solution of it
in front of the spectrum, we see that it cuts off
different rays to the latter. It would be quite
possible to mistake one green for the other, but
directly we analyze the white light which has
filtered through each by means of the spectrum,
we at once see that they differ. Mfience the
spectrum enables the eye to discmninate by
analysis what it would otherwise be unable to do.
Any coloured solution or transparent body may
be analyzed in the same way, and, as we shall
see subsequently, the intensity of every ray after
passing through it can be accurately compared
with the original incident light. There are some
cases, indeed the majority of cases, in which the
colour transmitted through a small thickness of

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COLOUR MEASUREMENT AND MIXTURE. 53

the material is different to that transmitted through
a greater thickness. For instance, a weak solution
of litmus in water is blue when a thin layer is ex-
amined, and red when it is a thicker or more con-
centrated layer. Bichromate of potash is more ruddy
as the thickness increases. This can be readily
understood by a reference to the law of absorption.
Suppose we have a thin layer of a liquid which
gives a purple colour when two simple colours,
red and blue, pass through it, and that this thin
layer cuts off one-quarter of the red and one-half
of the blue incident on it, another layer of equal
thickness will cut off another quarter of the three-
quarters of red passing through the first layer, and
half of the one-half left of the blue ; we shall thus
have nine-sixteenths of the red passing and only a
quarter of the blue. With a third layer we shall
have twenty-seven sixty-fourths of red and only
one-eighth of blue left, showing that as the thick-
ness of the hquid is increased the blue rapidly dis-
appears, leaving the red the dominant colour. Now
what is true of two simple colours is equally true of
any number of them, where the rates of absorption
differ from one another, and what is true for a
solution is true for a transparent solid. In some
opaque bodies, such as rocks, the reflected colour
often differs slightly from that of the same when
they are cut into thin and polished slices, through

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54 COLOUR MEASUREMENT AND MIXTURE.

which the light can pass. The reason is that when
opaque, light penetrates to a very small distance
through the surface, and is reflected back, whilst in
these layers the colour has to struggle through more
coloured matter, and emerges of a different hue.

The question why substances transmit some rays
and quench others, brings us into the domain of
molecular physics. Of all branches of physical
science this is perhaps the most fascinating and
the most speculative, yet it is one which is being
built up on the solid foundations of experiment
and mathematics, till it has attained an import-
ance which the questions depending on it fully
warrants. We have to picture to ourselves, in the
case in point, molecules, and the atoms composing
them, of a size which no microscope can bring to
view, vibrating in certain definite periods which are
similar to the periods of oscillation of the waves
of light. At page 26 we have given the lengths
of some of the waves which gfive the sensation of
coloured light. Now as light, of whatever colour
it may be, is practically transmitted with the same
velocity through air which has the same density
throughout, it follows that the number of vibra-
tions per second of each ray can be obtained by
dividing the velocity of light in any medium by
the wave-length. The following table gives roughly
the number of vibrations per second of the ether

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COLOUR MEASUREMENT AND MIXTURE. 55

giving rise to the colours fixed by the dark solar
lines.

Millions op

Name of Line.

Millions op

Vibrations

PER Second.

A in the Red.

395

^ » It

437

C II „ ... ...

458

D II Orange

510

E 1, Green

570

F „ Blue

618

G „ Violet

697

H „ Ultra-violet...

757

If we endeavour to guage what this rate of oscil-
lation means we shall scarcely be able to realize it,
even by a comparison with some physically measur-
able rate of vibration. A tuning-fork, for instance,
giving the middle C, vibrates 528 times per second.
Compare this with the number of vibrations of the
waves of light, and we still are as far as ever from
realizing it, yet the velocity of light, and the
lengths of the different waves have been accurately
determined ; the latter, although the much smaller
quantity, with even greater accuracy than the first.
These rates of vibration must therefore be — cannot
help being — at all events approximately true. This
being so, we know that some of the atoms of the
molecules at least, and perhaps in some cases, the

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S6 COLOUR MEASUREMENT AND MIXTURE.

molecules themselves, are vibrating at the same
rate as those waves of light, which they refuse to
allow to pass. If we have a child's swing beginning
to oscillate, we know that it is only by well-timed
blows that the extent of the swing is permanently
increased, and the energy exerted by the person
who gfives the well-timed blow is expended on pro-
ducing the increased amplitude. In the same way
if the rate of vibration of a wave of light is in accord
with that of a molecule or atom, the amplitude or
swing of the atom or molecule is increased, and the
energy of the wave and therefore its amplitude is
totally or partially destroyed; and as the ampli-
tude is a function of the intensity of the light, the
ray fails to be seen at all, or else is diminished in
brightness.

In what way the atoms vibrate where more than
one ray is absorbed is still a matter of speculation,
but no doubt as experimental methods are more
fully developed, and mathematicians investigate the
results of such experiments, we shall be able to
form a picture of the vibrations themselves. At
page 137 a speculation as to the reason why solids
or liquids can absorb more waves of light than one
which are adjacent to each other is put forward,
but it does not deal with the absorptions which
occupy various parts of the spectrum. Again,
too, we have the fact that the energy absorbed by

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COLOUR MEASUREMENT AND MIXTURE. $7

these atoms and molecules from the waves of light,
must show itself as work done on them — it may
be as heat or as chemical action. We shall see
by and by that in some cases, no doubt, at least
a part is expended in the latter form of work.

Perhaps this mode of looking at the question of
colour in objects may make the subject more
interesting to the reader than it at first appears to
be deserving. The whole subject is one which
enlarges the faculty of making mental pictures,
and this is one of the most useful forms of
scientific education.

But how can we distinguish between pigments
which to the eye are apparently the same? If
we dye paper with the green dye referred to, we
can place it in the spectrum, and we shall see that
the dye reflects differently to the white paper. In
fact we shall find that it refuses to reflect in those
parts of the spectrum which the transparent solu-
tion refused to transmit. So long as the light
passes through the dye-stuff", it is indifferent, as
regards ^the colour produced, whether the colouring
matter be at a distance from the paper or whether
the latter be dyed with it, as we can see at once.
If we place the solution of the dye in the reflected
beam of the apparatus and form a patch on the
screen, and alongside throw the patch of white
light from the integrated or recombined spectrum

58 COLOUR MEASUREMENT AND MIXTURE.

upon the dyed paper, it will be found that the
two colours are alike ; that is, the green-coloured
light on the white paper, or the white light on the
green paper are the same. Similarly we may
experiment on other dyes, such as magenta, log-
wood, &c., and we shall see that like results are
obtained. It should be said, however, that when
the paper is dyed with the colouring matter a
small quantity of white light will be reflected from
the surface of the paper itself. We may now say
that the general colour is given to a body by its
refusal to transmit or reflect, more or less com-
pletely, certain rays of the spectrum. Should the
solvent form a compound with the dye, perhaps
this would not be absolutely true, but in the large
majority of cases the statement is correct. When
we have bodies which are also fluorescent, this
statement would also have to be modified, but we
need not consider these for the present.

Another source of colour in objects, though very
rarely met with, and which for our object we need
not stay to explain in detail, is the interference of
light. Such is seen in soap-bubbles. Briefly it may
be said that the colours are due to rays of light
reflected from the inner surface of the film, which
quench other rays of light of the same wave-length
reflected from the outer surface. If two series of
waves of the same wave-length are going in the same

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COLOUR MEASUREMENT AND MIXTURE. 59

direction and from the same source, each of which
has the same intensity as the other, that is, having
the same amplitude, and it happens that the one
series is exactly half a wave-length behind the other,
then the crest of one wave in the first series will fill
up the trough of the other in the second series, and
no motion would result, and this lack of motion
means darkness, since it is the wave motion which
gives the sensation of light. If then we have white
light falling on two reflecting surfaces, such as the
front and back of a soap-film, part of the light will
be reflected from each, and if the film be of such
a thickness that the latter reflects light exactly ^
wave-length, | or f wave-length, &c., of some colour
behind the former, the colour due to that particular
wave-length will be absent from the reflected white
light, and instead of white light we shall have
coloured light, due to the combination of all the
colours less this colour, which is quenched.

A very pretty experiment to make is to throw
the image of a soap film on the screen, and to
watch the change in the colours of the film. Their
brilliancy increases as the film becomes thinner,
and the bands, which first appear close to each
other, separate, and then we see a large expanse
of changing colour, A soap solution should be
made according to almost any of the published
formulae, and a piece of flat card be dipped in it«

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60 COLOUR MEASUREMENT AND MIXTURE.

and be drawn across a ring of wire some inch in
diameter, or — what the writer prefers best — the
stop of a photographic lens. A film will form and
fill the aperture. The ring or stop may be placed
vertically in a clamp, and a beam of light caused
to fall at an angle of about 45 degrees on to the
film. If a lens be placed in the path of the re-
flected beam to form an image of the aperture, the
colours which the film shows can be exhibited to
an audience, if the diameter of the image be made

VlOLEi; CAEEN RED

Fig. 9. — Interference Bands.

four or five feet. Instead of this large image, a
small image may be thrown on the slit of the
spectroscope, by using a lens of a greater focal
length, and if the beam be so directed that it falls
on the axis of the collimator, a very fairly bright
spectrum may be also thrown on the screen. The
appearance of the spectrum is somewhat like that
shown in the above diagram (Fig. 9).

If we take a horizontal line across the spectrum.

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COLOUR MEASUREMENT AND MIXTURE. 6l

we shall see what particular colours are missing
from the reflected light which falls on the part of
the slit corresponding to that line. The colours
of some objects, such as of the opal, and the lovely
colouring of some feathers are due to interference
of light. The partial scattering of different rays
by small particles will also cause light to be
coloured, as we shall see in the experiments we
shall make to imitate the colour of sunlight at
various altitudes of the sun. We may, however,
take it as a rule that the colour of objects is
produced by the greater or less absorption of some
rays, and the reflection in the case of opaque bodies,
or the transmission, in the case of transparent
bodies, of the remainder.

dbyGoogk

CHAPTER VI.

Scattered Light — Sunset Colours — Law of the Scattering by
Fine Particles — Sunset Clouds — Luminosities of Sunlight
at different Altitudes of the Sun.

It is probable that we should be able to ascertain
approximately the true colour of sunlight (if we
may talk of the colour of white light) if we could
collect all the light from a cloudless sky, and con-
dense it on a patch of sunlight thrown on a screen.
For skylight is, after all, only a portion of the light
of the sun, scattered from small particles in the
atmosphere, part of the light being scattered into
space, and part to our earth. The small particles
of water fand dust — and when we say small we
mean small when measured on the same scale as me
measure the lengths of waves of light — differentiate
between waves of different lengths, and scatter the
blue rays more than the green, and the green than
the red ; consequently what the sun lacks in blue
and green is to be found in the light of the sky.

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COLOUR MEASUREMENT AND MIXTURE. 63

The effect that small water particles have upon
light passing through them can be very well seen in
the streets of London at night, when the atmosphere
is at all foggy. Gaslights at the far end of a street
appear to become ruby red and dim, and half-way
down only orange, but brighter, whilst close to they
are of the ordinary yellow colour, and of normal
brightness. When no fog is present the gaslights in
the distance and close to are of the same colour and
brightness, showing that their change in appearance
is simply due to the misty atmosphere intervening
between them and the observer. We can imitate
the Jight from the sun, after its passage through
various thicknesses of atmosphere, in a very perfect
manner in. the lecture-room, using the electric light
a$. a source. A condensing lens is put in front of
the lamp, and in front of that a circular aperture in
a plate. Beyond that again is a lens which throws
an enlarged image of the aperture on the screen,
which we may call our mock sun. If we place a
trough of glass, in which is a dilute solution of
hyposulphite of soda, carefully filtered from motes
as far as possible, in front of the aperture, we
have an image of the aperture unaffected by the
insertion of the solution. The white disc on the
screen will, as we have said before, be a close
approximatiop to sunlight on a May-day about
noon, when the sky is clear. By dropping into

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64 COLOUR MEASUREMENT AND MIXTURE.

the trough a little dilute hydrochloric acid, a change
will be found to come over the light of the mock
sun; a pale yellow colour will spread over its
surface, and this will give way to an orange tint,
and at the same time its brightness will diminish.
Gradually the orange will give place to red, the
luminosity will be very small, being of the same
hue as that seen in the sun when viewed through
a London fog. Finally the last trace of red will
so mingle with the scattered white light that the
image will disappear, and then the experiment is
over.

If we track the cause of this change of colour
in our artificial sun, we shall find that it is due
to minute particles of sulphur separating out
from the solution of hyposulphite, and the longer
the time that elapses the more turbid the dilute
solution will become. This experiment exem-
plifies the action of small particles on light
Examining the trough it will be found that whilst
the light which passes through the solution princi-
pally loses blue rays, the light which is scattered
from the sides is almost cerulean in blue, and can
well be compared with the light from the sky. We
can analyze the transmitted light very readily by
focussing the beam from the positive pole of the
electric light on to the slit of our colour appa-
ratus, and placing the lens L« (Fig. 6) in position

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COLOUR MEASUREMENT AND MIXTURE. 65

to form the large spectrum on the screen. We can
also show the colour of the light which goes to
form the spectrum, by sending the patch of light
reflected from the first surface of the first prism
just above it. We thus have the spectrum and
the light forming the spectrum to compare with
one another. Using this apparatus and inserting
the trough of dilute hyposulphite in the beam,
the spectrum is of the character usually seen with
the electric light; but on dropping the dilute
hydrochloric acid into the solution the same hues
fall on the slit of the spectroscope which fell upon
the screen to form the mock sun, and the spectrum
is seen to change as the light changes from white
to yellow, and from yellow to red. First the violet
will disappear, the blue and the green being
dimmed, the former most however ; then the blue
will vanish to the eye, the green becoming still
less luminous, and the yellow also fading; the
green and yellow will successively disappear,
leaving finally on the screen a red band alone,
which will be a near match to the colour of the
unanalyzed light, as may be seen by comparing it
with the adjacent patch formed from the reflected
beam.

We have here a proof that the succession of
phenomena is caused by a scattering of the shorter
wave-lengths of light, and that the shorter the

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66 COLOUR MEASUREMENT AND MIXTURE.

waves are the more they are scattered. It has
been found theoretically by Lord Rayleigh that
the scattering takes place in inverse proportion to
the fourth power of the wave-length ; thus, if two
wave-lengths, which may be waves in the green
and violet, are in the proportion of three to four,
the former will be scattered as ~ to ^, or as 256
to 81, which is approximately as three to one.
Consequently if the green in passing through a
certain thickness of a turbid medium loses one-half
the violet in passing through the same thickness
will lose five-sixths of its luminosity. The inverse
fourth powers of the following wave-lengths, which
are within the limits of the whole visible spectrum,
are shown below.

X I 7000 I 6000 I 5000 I 4000

I I I -504 I -260 I -107

Supposing X7000 by the scattering of small
particles loses one-tenth of its luminosity, then
X6000 would have "454 of its original brightness ;
XSOOO, '234; and X4000, '095 ; that is, whilst X7000
would lose one-tenth only of its luminosity, X4000
in the violet would retain not quite one-hundredth
of its brightness.

During the years 1885, 1886, and 1887, the writer
measured the luminosity of the solar spectrum at

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COLOUR MEASUREMENT AND MIXTURE. 67

different times of the year, and at different hours
of the day (see Phil. Trans. 1887: "Transmission
of Sunlight through the Earth's Atmosphere *'), and
from the results
he found that the
smallest coeffi-
cient of scattering
for one atmos-
phere at sea-level
for each wave-
length was '0013,
when X~* was for
convenience sake
multiplied by 10"
(thus xeooo"* on
this scale was
77-2), and that the
mean was '0017.

The following
table shows the
loss of light for
the ra)^ denoted
by the principal
lines given at
page 26, using
this . last coefficient for different air thicknesses.
This is equivalent to giving the intensity of the rays
of sunlight when the sun is at different altitudes.

•5

•11

■a

§•

»o

■♦
?

"♦

10
00

•^

«o

.5^

P>3

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68 COLOUR MEASUREMENT AND MIXTURE.

The sun traverses the following thicknesses of
atmosphere when it is at the angles shown above
the horizon.

I atmosphere 90®

2
3
4
5
6

7
8

30^
1930
14-30
11-30
9-30

8-30
7*30

It traverses thirty-two atmospheres when it is

4000 0^0 5000 50^ 6000 ^^° 7000
Fig. 10. —Absorption of Rays by the Atmosphere.

very nearly setting. Bougier and Forbes have
calculated that the extreme thickness of the

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COLOUR MEASUREMENT AND MIXTURE. 69

atmosphere, traversed by its light when the sun is
on the horizon, is approximately 35 J atmospheres.
The absorption shown by 32 atmospheres will
therefore be very close to that which would be
observed at sunset on an ordinary day, and it
will be seen that practically all rays have been
scattered from the light, except the red, and a little
bit of the orange.

As to the luminosity of the sun at these different
altitudes, we can easily find it by reducing the
luminosity curve of the sun at some known alti-
tude by the factors in the table just given, for as
many wave-lengths as we please, and thus con-
struct another curve. The area of the figure thus
obtained would be a measure of the total luminosity
on the same scale as the area of the luminosity
curve from which it was derived.

The following are the approximate luminosities
of the sun when the light shines

I oat

mospheres

•840

» •

70s

•594

» *

•496

it •

•417

»i •

•303

•256

» •

•215

•002

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70 COLOUR MEASUREMENT AND MIXTURE.

It will thus be seen that the sun is 420 less
bright just at sunset than it is if it were to shine
directly overhead, and about 350 times brighter
than it is for a winter sun in a cloudless and mist-
less sky at twelve o'clock, for the altitude of the
sun in our latitude is about 30° at that time, and
corresponds with a thickness of two atmospheres,
through which the sun has to shine. We all know
that to look at the sun at any time near noon in a
cloudless sky dazzles the eyes, but that near sunset
it may be looked at with impunity. The reduction
in luminosity explains this fact.

The distribution of the scattering particles in
the atmosphere is very far from regular. As we
ascend, the particles get more sparse, as is shown
by the less scattering that takes place of the blue
rays compared with the red. Thus at an altitude
of some 8000 feet the mean coefficient of scatter-
ing is about '0003, instead of '0017, which it is at
sea-level. It must be recollected that there is only
about three-fourths of the air above us at 8000
feet, and it is less dense. There will therefore be a
diminution of particles not only because there is less
air, but because the air itself is less capable of keep-
ing them in suspension. Up to 3000 or 4000 feet
there is no very great marked difference in the scat-
tering of light, as observations carried on during five
years have shown; but above that the scattering

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COLOUR MEASUREMENT AND MIXTURE. /I

rapidly diminishes, and at 20,000 feet it must be
very small indeed, if the diminution increases as
rapidly as has been found it does at the altitude of
8000 feet.

We must repeat once more that the blue of the
sky is principally if not entirely due to the pre-
sence of these particles, the rays scattered by them,
which are principally the blue rays, being reflected
back from them, giving the sensation of blue which
we know as sky-blue. The greater the number of
these fine particles that are encountered by sun-
light, the greater the scattering will be, and the
bluer the sky. It is more than probable that the
blue sky of Italy, so proverbial for being beauti-
ful, is due to this cause, since from its geographical
position the small particles of water must be very
abundant there.

Carrying this argument further, we should expect
that as we mount higher the blue would become
more fully mixed with the darkness of space, and
this Alpine travellers will tell you is the case. At
heights of 12,000 feet or more, on a clear day, the
sky seems almost black, and it is no uncommon
thing to see this admirably rendered in photographs
of Alpine scenery when taken at a height. Many
of the late Mr. Donkin's photographs show this in
great perfection, as also Signor Sella's.

Before quitting thi3 subject we may call attention

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72 COLOUR MEASUREMENT AND MIXTURE.

not only to the colour of the sun itself at sunset,
but also to the colouring of the sky which accom-
panies the sun as it sinks. This colouring is often
different to the colour that the sun itself assumes ;
but we can easily show that the effects so won-
derfully beautiful are entirely dependent on this
scattering of light by these small ihtervening par-
ticles in the air. We often see a ruddy sun, and
perhapj nearly in the zenith, or even further away
fiom the sun, clouds of a beautiful crimson hue,
lying on a sky which appears almost pea-green,
whilst nearer to the sun the sky is a brilliant
orange, which artists imitate with cadmium yellow.
Let us fix our attention first on the crimson cloud.
The clouds of which the colouring is so gorgeous
are often not looo feet above us, and were we to be
at that altitude we should see the sun not quite so
ruddy as we see it from the earth, and the cloud
would consequently be illuminated by the sun with
a more orange tint ; but the light reflected from the
cloud to our eyes has to pass through, say lOOO feet
of dense atmosphere, and thus the total atmosphere
that the light traverses in the latter case is always
greater than the air thickness through which the
direct light from the sun has to pass ; hence more
orange is cut off, and the light reflected from the
cloud is redder. This red, however, will not account
for the brilliant crimson and purples which we so

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COLOUR MEASUREMENT AND MIXTURE. 73

often see. It has to be remembered that not sun-
light alone illumines the cloud, but also the blue
light of the sky. The feebler the intensity of the
red,, the more will the blue of the sky be felt in
the mixture of light which reaches our eye's, and
consequently we may have any tint ranging from
crimson to purple, since red and blue make these
hues, according to the proportions in which they
are mixed.

Now let us see how we get the brilliant orange
of the sky itself. When the evening is perfectly
clear and free from mist .and cloud, the orange in
the sky is very feeble, showing that the intensity
depends upon their presence. Now a look at the
table will show that the sun is very close to the
horizon when it becomes ruddy under normal con-
ditions ; but that when the light traverses a thick-
ness of eight atmospheres, the blue and violet, and
most of the green, are absent, leaving a light of
yellowish colour. To traverse eight atmospheres
the light has only to come from a point some eight
degrees above the horizon. When the sun is near
the horizon, it sends its rays not only to us and over
us, but in every direction ; and an eye placed some
few thousand feet above the earth would see the
sun almost of its mid-day colour, for sunset colours
of the gorgeous character that we see at sea-level
are almost absent at high altitudes. If a cloud or

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74 COLOUR MEASUREMENT AND MIXTURE.

mist were at such an altitude the sunlight would
strike it, and whilst only a small portion would be
selectively scattered, owing to the general grossness
of the particles, the major part would be reflected
back to our eyes, and come from an altitude of
over eight to ten degrees, and would therefore,
after traversing the intervening atmosphere, reach
us as the orange-coloured light of which we
have just spoken. The clouds which are orange
when near the sun, are usually higher than those
which are simultaneously red or purple. The
pea-green colour of the sky is often due to con-
trast, for the contrast colour to red is green, and
this would make the blue of the sky appear de-
cidedly greener. Sometimes, however, it is due to
an absolute mixture of the blue of the sky and
the orange light, which illuminates the same haze.
In the high Alps it is no uncommon occurrence
for the snow-clad mountains to be tipped with
the same crimson we have described as colouring
the clouds, and this is usually just after sunset,
when the sun has sunk so low beneath the
horizon that the light has to traverse a greater
thickness of dense air, and consequently to pass
through a larger number of small particles than it
has when just above the horizon. In this case
the red of the sunlight mixes with blue light of the
sky, and gives us the crimson tints. The deeper

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COLOUR MEASUREMENT AND MIXTURE. 75

and richer tints of the clouds just after sunset
are also due to the same causfe, the thickness of
air traversed being greater. •

It is worth while to pause a moment and think
what extraordinary sensual pleasure the presence
of the small scattering particles floating in the air
causes us ; that without them the colouring which
impresses itself upon us so strongly would have
been a blank, and that artists would have to rely
upon form principally to convey their feelings of
art. Indeed without these particles there would
probably be no sky, and objects would appear of
the same hard definition as do the mountains in
the atmosphereless moon. They would be only
directly illuminated by sunlight, and their shadows
by the light reflected from the surrounding bright
surfaces.

dbyGoOgjf

CHAPTER VII.

Luminosity of the Spectrum to Normal-eyed and Colour-
blind Persons — Method of determining the Luminosity
of Pigments — Addition of one Luminosity to another.

The determination of the luminosity of a coloured
object, as compared with a colourless surface
illuminated by the same light, is the determin-
ation of the second colour constant. We will
first take the pure spectrum colours, and show
how their luminosity or relative brightness can be
determined. Viewing a spectrum on the screen,
there is not much doubt that in the yellow there
is the greatest brightness, and that the brightness
diminishes both towards the violet and red. To-
wards the latter the luminosity gradieat is evidently
more rapid than towards the former. This being the
case, it is evident that, except at the brightest part
there are always two rays, one on each side of the
yellow, which must be equally luminous. If the
spectrum be recombined to form a white patch

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COLOUR MEASUREMENT AND MIXTURE. ^^

upon the screen, and the slide with the slit be
passed through it, patches of equal area of the
different colours will successively appear ; but the
yellow patch will be the brightest patch. If the
patch formed by the reflected beam be superposed
over the colour patch, and the rod be interposed,
we get a coloured stripe alongside a white stripe,
and by placing our rotating sectors in the path
of the reflected beam, the brightness of the latter
can be diminished at pleasure. Suppose the sectors
be set at 45®, which will diminish the reflected beam
to one-quarter 6f its normal intensity, we shall find
some place in the spectrum, between the yellow
and the red, where the white stripe is evidently less
bright than the coloured stripe, and by a slight
shift towards the yellow, another place will be
found where it is more bright. Between these two
points there must be some place where the bright-
ness to the eye is the same. This can be very
readily found by moving the slit rapidly back-
wards and forwards between these two places of
"too dark" and "too light," and by making the path
the slit has to travel less and less, a spot is finally
arrived at which gives equal luminosities. The
position that the slit occupies is noted on the scale
behind the slide, as is also the opening of the
sectors, in this case 45". As there is another posi-
tion in the spectrum between the yellow and the

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78 COLOUR MEASUREMENT AND MIXtURE.

violet, which is of the same intensity, this must be
found in the same manner, and be similarly noted.
In the same way the luminosities of colours in the
spectrum, equivalent to the white light passing
through other apertures of sectors, can be found,
and the results may then be plotted in the form
of a curve. This is done by making the scale of
the spectrum the base of the curve, and setting up

S7 5S 55^j54 88^52. 51 ^50^49 48 47^^40 4S ^^^'^9^2

Fig. II. — Luminosity Curve of the Spectrum of the Positive Pole
of the Electric Light.

at each position the measure of the angular aperture
of the sector which was used to give the equal
luminosity or brightness to the white. By joining
the ends of these ordinates by lines a curve is
formed, which represents graphically the luminosity
of the spectrum to the observer. In Fig. 1 1 the
maximum luminosity was taken as lOO, and the
other ordinates reduced to that scale. The outside

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 79

curve of the figure was plotted from observa-
tions made by the writer, who has colour vision
which may be considered to be normal, as it coin-
cides with observations made by the majority of
persons. The inner curve requires a little explan-
ation, though it will be better understood when the
theory of colour vision has been touched upon/

The observer in this case was colour-blind to the
red, that is, he had no perception of red objects as
red, but only distinguished them by the other colours
which were mixed with the red. This being
premised, we should naturally expect that his
perception of the spectrum would be shortened,
and this the observations fully prove. If it
happened that his perceptions of all other colours
were equally acute with a normal-eyed person, then
his illumination value of the part of the spectrum
occupied by the violet and green ought to be the
same as that of the latter. The diagram shows
that it is so, and the amount of red present in
each colour to the normal-eyed observer is shown
by the deficiency curve, which was obtained by sub-
tracting the ordinates of colour-blind curve from
those of the normal curve. There are other persons
who are defective in the perception of green, and
they again give a different luminosity curve for the
spectrum. These variations in the perception of
the luminosity of the different colours are very

Digitized by LjOOQ IC

8o COLOUR MEASUREMENT AND MIXTURE.

interesting from a physiological point of view, and
this mode of measuring is a very good test as to
defective colour vision. We shall allude to the
subject of colour-blindness in a subsequent chapter.
The following are the luminosities for the
colours fixed by the principal lines of the solar
spectrum, and for the red and blue lines of
lithium, to which reference has already been
made.

Line.

Colour. .

Luminosity.

Normal
Eye.

Red
Colour
Blind.

Very dark Red

Red (Crimson)

I'O

Red Lithium

Red (Crimson)

8-5

•5

Red (Scarlet)

Orange

Green

20*6

98-5

50-0

53*o
490

Blue Green

7*0

7-0

Blue Lithium

Blue

1*9

Violet

•6

Faint Lavender

—

The failure of the red colour-blind person to
perceive red is very well shown from this table.
It will for instance be noticed that he perceives
about one-tenth of the light at C which the normal-
eyed person perceives.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 8 1

I A modification of this plan can be employed for

measuring the luminosity of the spectrum, and it is
excessively useful, because we can adapt it to the
measurement of colours other than these simple
ones. In the- plan alre?idy explained it was the
colour in the patch that was altered, to get an
equal luminosity with a certain luminosity of white
light. In the modified plan the luminosity of the
white light is altered, for the luminosity of the
shadow illuminated by the reflected beam can
be altered rapidly at will by opening or closing
the apertures of the sectors whilst it is rotating.
The slit, in the slide is placed in the spectrum at
any desired point, and the aperture of the sectors
altered till equal luminosities are secured. The
readings by this plan are very accurate, and give
the same results as obtained by the previous
method employed.

It must be remembered that we have so far
dealt with colours which are spectrum colours,
and which are intense because they are colours
produced by the spectrum of an intensely bright
source of light. By an artifice we can deduce
from this curve the luminosity curve of the spec-
trum of any other source of light. If by any
means we can compare, inter se, the intensity of the
same rays in -two different sources of light, one
being the electric light, we can evidently from the

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82 COLOUR MEASUREMENT AND MIXTURE.

above figure deduce the luminosity curve of the
spectrum of the other source of light (see p. 109).

We can now show how we can adapt the last
method to the measurement of the luminosity of
the light reflected from pigments.

Suppose the luminosity of a vermilion-coloured
surfa.'e had to be compared with a white surface
when both were illuminated, say by gaslight, the
followin;:j procedure is
adopted. A rectangular
space is cut out of black
paper (Fig. 12) of a size
such that its side is rather
less than twice the breadth
of the rod used to cast a
shadow: a convenient size
is about one inch broad by
three-quarters of an inch
in height. One-half of the aperture is filled with a
white surface, and the other half with the vermilion-
coloured surface. The light L (Fig. 13) illuminates
the whole, and the rod R, a little over half an inch
in breadth, is placed in such a position that it casts
a shadow on the white surface, the edge of the
shadow being placed accurately at the junction of
the vermilion and white surface. A flat silvered
mirror M is placed at such a distance and at such an
angle that the light it reflects casts a second shadow

Fig. 12.— Rectangles of White
and Vermilion.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 83

on the vermilion surface. Between R and L are
placed the rotating sectors A. The white strip is
caused to be evidently too dark and then too light
by altering the .

aperture of the sP"---. jf\ ,

sectors, and an ■ '^ """^-^ 1

oscillation of dim- *"**-^ I

inishing extent is yfe

rapidly made till Fig. 13.— Arrangement for measuring
the two shadows the Luminosities of Pigments.

appear equally luminous. A white screen is next
substituted for the vermilion and again a com-
parison made. The mean of the two sets of
readings of angular apertures gives the relative
value of .the two luminosities. It must be stated,
however, that any diffused light which might
be in the room would relatively illuminate the
white surface more than the coloured one. To
obviate this the receiving screen is placed in a box,
in the front of which a narrow aperture is cut just
wide enough to allow the two beams to reach the
screen. An aperture is also cut at the front angle
of the box, through which the observer can see the
screen. When this apparatus is adopted, its
efficiency is seen from the fact that when the
apertures of the rotating sectors are closed the
shadow on the white surface appears quite black,
which it would not have done had there been

Digitized by LjOOQ IC

84 COLOUR MEASUREMENT AND MIXTURE.

dififused light in any measurable quantity present
within the box. The box, it may be stated, is
blackened inside, and is used in a darkened room.
The mirror arrangement is useful, as any variation
in the direct light also shows itself in the reflected
light. Instead of gaslight, reflected skylight or
sunlight can be employed by very obvious artifices,
in some cases a gaslight taking the place of the
reflected beam. When we wish to measure lumin-
osities in our standard light, viz. the light emitted
from the crater of the positive pole of the arc-light,
all we have to do is to place the pigment in the
white patch of the recombined spectrum, and illu-
minate the white surface by the reflected beam,
using of course the rod to cast shadows, as just
described. The rotating sectors must be placed in
either one beam or the other, according to the
luminosity of the pigment

The luminosities of the following colours were
taken by the above method, and subsequently we

shall have to use their values.

Electric Light.

White

ICO

Vermilion

Emerald Green

Ultramarine ...

4-4

Orange

3yi

Black

3*4

„ (different surface)

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 85

Suppose we have two or more colours of the
spectrum whose luminosities have been found, the
question immediately arises, as to whether, when
these two colours are combined, the luminosity of
the compound colour is the sum of the luminosities
of each separately. Thus suppose we have a slide
with two slits placed in the spectrum, and form a
colour patch of the mixture of the two colours
and measure its luminosity, and then measure the
luminosity of the patch first when one slit is
covered up, and then the other. Will the sum of
the two latter luminosities be equal to the measure
of the luminosity of the compounded colour
patch ? One would naturally assume that it would,
but the physicist is bound not to make any assump-
tions which are not capable of proof ; and the truth
or otherwise is perfectly easy to ascertain, by em-
ploying the method of measurement last indicated.
Let us get our answer from such an experiment

Colours

Observed

Measured,

Luminosity.

R ... .■

203-0

38-5

8-5

(R + G)

242

(G + V)

(R + V)

214

(R + G + V) ..

250

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86 COLOUR MEASUREMENT AND MIXTURE.

Three apertures were employed, one in the red,
another in the green, and the third in the violet,
and the luminosity was taken of each separately,
next two together, and then all three combined,
with the results given above.

The accuracy of the measurements will perhaps be
best shown by adding the single colours together,
the pairs and the single colours, and comparing
these values with that obtained when the three
colours were combined. When the pairs are shown
they will be placed in brackets ; thus (R + G)
means that the luminosity of the compound colour
made by red and green are being considered.
R + G + V = 2500

(R + G) + V = 250-5

(R + V) + G = 252-5

(G + V) + R = 2480

(R + G + V) = 250-0
The mean of the first four is 250*25, which is
only 1^% different from the value of 250 obtained
from the measurement of (R + G + V) combined.
Other measures fully bore out the fact that the
luminosity of the mixed light is equal to the sum
of the luminosities of its components. It is true
that we have here only been dealing with spectrum
colours, but we shall see when we come to deal
with the mixture of colours reflected from pig-
ments that the same law is universally true.

dbyGoogk

COLOUR MEASUREMENT AND MIXTUl^E. 8/

It will be proved by and by that a mixture of
three colours, and sometimes of only two colours,
be they of the spectrum or of pigments, can
produce the impression of white light. If then we
measure all the components but one, and also the
white light produced by all, then the luminosity
of the remaining component can be obtained by
deducting the first measures from the last. For
instance, red, green and violet were mixed to form
white light. The luminosity of the white being
taken as lOO, the red and violet were measured
and found to have a luminosity of 44*5 and 3 re-
spectively. This should give the green as having
a luminosity of 52*5. The green was measured
and found to be 53, whilst a measurement of the
red and green tegether gave a luminosity of 96* 5
instead of 97.

dbyGoogk

CHAPTER VIII.

Methods of Measuring the Intensity of the Different Colours
of the Spectrum, reflected from Pigmented Surfaces —
Templates for the Spectrum.

We will now proceed to demonstrate how we can
measure the amount of spectral light reflected by
different pigments. Let us take a strip of card
painted with a paste of vermilion, leaving half the
breadth white ; and similarly one with emerald
green. If we place the first in the spectrum so that
half its breadth falls on the red, and the other half
on the white card, we shall see that apparently the
red and orange rays are undiminished in intensity
by reflection from the vermilion, but that in the
green and beyond but very little of the spectrum is
reflected. With the emerald green placed similarly
in the spectrum, the red rays will be found to
be absorbed, but in the green rays the full in-
tensity of colour is found, fading off in the blue.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 89

What we now have to do is to find a method
of comparing the intensities of the different rays
reflected from the pigments, with those from
the white surface. We will commence with the
second of the two methods which the writer devised
with this object, and then describe the first, which
is more complex. Suppose we have, say a card

FfO. 14. — Measurement of the Intensity of Rays reflected from white
and coloured surfaces.

disc three inches in diameter, painted with the pig-
ment whose reflective power has to be measured,
and place it on a rotating apparatus with black
and white sectors of say five inches diameter, and
capable of overlapping so as to show different pro-
portions of black to white (see Fig. 42). If we
throw a colour patch (shown in Fig. 14 as the area
inside the dotted square) on the combination of black

dbyGoogk

90 COLOUR MEASUREMENT AND MIXTURE.

and white, and at the same time on the pigmented
disc, it is probable that either one or other will be
the brighter. By moving the slit along the spectrum
it is evident, however, that a colour can be found
which is equally reflected from them both whilst
rotating. Take as an example the sectors as set at
two parts white, to one part black, the centre disc
being vermilion, the slit is moved along the spec-
trum until such a point is reached that the colour
reflected from the ring and the disc appears of the
same brightness, for it must be recollected that they
cannot differ in hue, as the light is monochromatic.
It will be found that the place where they match
in brightness is in the red, the exact position being
fixed by the scale at the back of the slide. Taking
the proportion of black to white as three to one,
the match will be found to take place in the orange.
Increasing the proportion of black more and more,
a point will be reached where the reflection takes
place uniformly along the blue end of the spectrum,
this will be from the green to the end of the violet
By sufficiently increasing the number of matches
made, a curve of reflection can be made showing
the exact proportion of each ray of the spectrum
that is reflected. The uniform reflection along
the blue end of the spectrum shows that a cer-
tain amount of white light is reflected from the
pigment.

Digitized by LjOOQ IC

COLOUR MEASUREMENT AND MIXTURE. 9I

Next taking the emerald green disc, if we adopt
the same procedure it will be found that for some
shades of the ring there are two places in the
spectrum from which the colours reflected give the
same brightness. By plotting curves in exactly
the same way as that shown for the curve of lumin-
osity at page 78, substituting for the open aperture
of the sector the angular value of the white used,
we can show graphically the correct reflection
for each part of the spectrum. Sometimes three
places in the spectrum will be read, as giving
equal reflections from the coloured disc and the
grey ring.

The accompanying figures show the results ob-
tained for reflection from vermilion, emerald green,
and French blue, after having made a correction
for the white by adding the amount which the
black reflects.

The scale is that of the prismatic spectrum
employed. On page 46 we stated that a white
surface could be made to appear darker than a
black surface, by illuminating the latter and cut-
ting off the light from the former. By placing
the black surface in place of one of the coloured
ones, as shown in page 82, the luminosity of the
black surface can be ascertained. In this case it
was found that almost exactly 5% of the white light
from the crater of the positive pole was reflected.

Digitized by LjOOQ IC

92 COLOUR MEASUREMENT AND MIXTURE.

OQOpOoOOOO. O

\-'f-X

■HOI

^ ill

. p- §

o s

e
I

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 93

In the table the original measures are shown, and
also the corrected measures, and for convenience
sake the intensity of every ray throughout the
length of the spectrum reflected from white, has
been taken as 100. The position of the reference
lines on the scale (Fig. 15) are as follows —

B=ipi,C=96-2S,D = 89,E=79*9>F = 7i'S>G = S3S.

VERMILION.

White Sectors.

Reading of
Spectrum

Original Setting.

White cor-

Corrected

rected FOR

White

Scale.

White.

Black.

100.

350

27-5

7-65

l'^ ^

340

37-0

10*15

330

46-5

12-95

86-2

310

65-5

i8*io

88-0

290

84-5

23*50

887

270

103*5

29*7

89-5

120

240

132-0

37*2

90-3

150

210

i6o*5

45*0

180

189*0

52-5

91*6

210

150

2175

60*2

92-5

220

140

227*0

63 -2

93 '5

230

130

236-5

66*2

94-5

240

120

246*0

68*5

230

130.

236-5

66-2

977

210

150

217-5

60*2

loo-o

dbyGoogk

94 COLOUR MEASUREMENT AND MIXTURE.

EMERALD GREEN.

Whitb Sectors.

Reading op

Original

Setting.

White cor-

Corrected

Spectrum

rected FOR

White

Scale.

White.

Black.

100.

350

27-5

7-65

340

370

10-15

330

465

12-95

310

65-5

18-10

57-5

290

84-5

23-5

60-0

270

103-5

297

63s

250

122'5

347

65-5

130

230

141-5

39-5

67-s

150

210

160-5

45-0

68-5

170

190

179-5

50-0

190

170

195-5

54-7

73*5

210

150

217-5

60-2

75-0

220

140

227

632

220

140

227

63-2

210

150

217-5

60-2

190

170

I98-S

54*7

170

190

179-5

50-0

150

210

160-5

45-0

130

230

141-5

39-5

250

122-5

34-7

86-5

270

103-5

297

87-5

290

845

23-5

88-5

310

65-5

18-10

90-0

330

465

12-95

340

37-0

10-15

350

27-5

7-65

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 95

FRENCH ULTRAMARINE BLUE.

White Sectors. .

Reading op

Original

Setting.

White cor-

Corrected

Spectrum

RFPTirn TSTlR

Whttp

Scale.

White.

Black.

BLACK.

VV XXiX £>

100.

360

i8-o

5"o

350

27-5

7-65

340

37*0

io"i5

330

46-5

"•95

320

56-0

156

300

7S-0

207

725

280

940

25-5

70-5

100

260

113-0

325

120

240

132-0

37'2.

66-s

140

220

151-0

42-3

62s

160

»oo

170-0

47 '4

59-5

170

190

179*5

50-0

160

200

170-0

47*4

140

220

151*0

42-3

360

180

S-o

' 10

350

27-5

7-65

340

37'o

10*15

330

46-5

12-95

These three measurements have been given in
full, since they will be useful for reference when
other experiments are described.

When we have to measure the colour transmitted
through coloured bodies, we have to adopt a slightly
different plan, which is extremely accurate. The

dbyGoogk

96 COLOVR MEASUREMENT AND MIXTURE.

first thing necessary is to make some arrangement
whereby two beams of identical colour — that is, of
the same wave-length — reach the screen, one of
which passes through the transparent body to be
measured, and the other unabsorbed. If we in
addition have some means of equalizing the in-
tensity of the two beams, we can then tell the
amount cut off by the body through which one
beam passes. The method that would be first
thought of would be to use two spectra, from two
sources of light; but should we adopt that plan
there would be no guarantee that the spectra would
not var>' in intensity from time to time. The point
then that had to be aimed at was to form two
spectra from the same source of light, and with the
same beam that passes through the slit of the
collimator. Here we are helped by the property
of Iceland spar, which is able to split up a ray into
two divergent rays. By placing what is called a
double-image prism of Iceland spar at the end of
the collimator, we get two divergent beams of light
falling on the prisms, and by turning the double-
image prism we are able to obtain two spectra on
the screen of the camera one above the other, and
if the slit of the slide be sufficiently long two beams
would issue through it of identical colour, and
separated from one another by a dark space, the
breadth of which depends on the length of the slit

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 97

of the collimator. It is to be observed that by this
arrangement we have exactly what we require : a
light from one source passes through the same
slit, is decomposed by the same prisms, and as the
beams diverge in a plane passing through the slit of
the collimator, the length of spectrum is the same.
The problem to solve is how to utilize these two
spectra now we have got them. We can make the
light from the top spectrum pass through the
coloured body by the following artifice. Let us
place a right-angled prism in front of the top slit,
reflecting say the beam to the right, and after it
has travelled a certain distance, catch it by another
right-angled prism, and thus reflect it on to the
screen. Already in the path of the ray, issuing
through the slit from the bottom spectrum, the lens
L^ is placed, forming a square patch on the screen.

Fig. 16.— Method of obtaining two Patches of identical Colour.

By placing a similar lens in the path of the other ray
after reflection from the second right-anglgd PQsm,
we can superpose a second patch of the sairosLi^GjS^v

vGoogI|^;

98 COLOUR MEASUREMENT AND MIXTURE.

over the first patch, and by putting a rod in the
path of the two beams we can have as before two
shadows side by side, but this time each illuminated
by the same colour. One shadow will be more
strongly illuminated than the other, owing to the
different intensities of beams into which the double-
image prism splits up the primary ray. The two,
however, can be equalized by placing a rotating
apparatus in the path of one of the beams. When
equalized the sector is read off, and tells us how
much brighter one spectrum is than the other.
Thus suppose in the direct beam the sectors had
to be closed to an angle of So"", to effect this, the
bottom spectrum would be -go* or 2*25 times brighter
than the bottom spectrum. It should be noted
that as the two spectra are formed by the identical
quality of light, this same ratio will hold good
throughout their length. If it does not, it shows
that the double-image prism is not in adjustment,
and that the same rays are not coming through the
slit in the slide, and it must be rotated till the read-
ings throughout are the same. One of the most
sensitive tests for adjustment is to form a patch
with orange light, when the slightest deviation from
adjustment will be seen by the two patches differing
in hue.

We can now place the coloured transparent
object in the path of the beam which is most

Digitized by VjOOQ IC

COLOUR MfiASUREMfiNT AND MlXTURfe. 99

convenient, and by again equalizing the shadows,
measure the amount it cuts off; this we can do
for any ray we choose. As both right-angled prisms
can be attached to the card or slide which moves
across the spectrum, nothing besides the card need
be moved. In the following diagram we have the
proportion of rays transmitted by the three dif-
ferent glasses, red, green, and blue, in terms of the
unabsorbed spectrum. Take for instance on the

— .

ifn

'hit

1 L

ahl

= 7C

iroi

i/t

SpB

:tn

■^

'*\

h/\

.*-

•?y

•'\n

B J7 16 J$ 14 /d 12 it to 6 8 1

'65482

I 3

Fig. 17.— Absorption by Red, Blue, and Green Glasses.

scale of the spectrum the number 11. The curve
shows that at that particular part of the spectrum
which lies in the blue, the blue glass only allowed
i5o or TF of the ray to pass, whilst the green glass
allowed ^ or tV to pass. So at scale No. 4 in the
orange, through the blue only 2% was transmitted,
through the green glass 4%, and through the
red 20%.

dbyGoogk

too COLOUR MEASUREMENT AND MIXtURfi.

^d^"

COLOUR MEASUREMENT AND MIXTURE. lOI

From such curves as these we can readily derive
the luminosity curves of the spectrum, after the
white light has passed through the coloured object.
All we have to do is to alter the ordinates of the
luminosity curve of whife light in the proportion to
the intensities of the rays before and after passing

too

OWhJtt

90
80
70

$0
SO
40
CO
26

90
80

'?-i

3--

^0^

"**'

!•'

L I'-i'^^viJ.

*^«

^yso ^ 7sc^

^ P* '^7oa>^J

d A

i I ^ ill fin I

X. Vennilion. a. Carmine. j. Mercuric Iodide.
4. Indian Red.

Fig. 19.

through the object. It will be seen that when the
luminosity curve of the spectrum of any source is
known, this method holds good.

The intensity of the different rays of the spec-
trum reflected from metallic surfaces can also be
measured, if for the first or second right-angled

d by Google

102 COLOUR MEASUREMENT AND MIXTURE.

prism a small piece of the metal is substituted,
using it as a reflecting surface, as can also the rays
reflected from any surface which is bright and
polished. In Fig. i8 the dotted curves show the
luminosity of the spectrum reflected from the dif-
ferent metals, curve V being that of white light.

^ ^ 9

<• Gamboge. 2. Indian Y«llow. 3. Cadmium Vello\V.
4. Yellow Ochre.

Fig. 20.

These curves are derived by reducing the ordinates
of curve V proportionately to the intensity curves.
Thus at 49 brass reflects 77""/^ of the light, and the
luminosity of the white is 80. The luminosity of
the light from the brass is therefore -ftV of 80, or

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. IO3

61. This shows the method which is adopted, of
deducing luminosities from intensities.

The light reflected from pigments can also be
measured by the same plan. The procedure
adopted is that carried out when measuring their
luminosities, viz. to cause the ray from one spec-

100

90
80

lOOWhitty

SO
20
10

^M*

■1 .

:'^

J-

"S,

, 1

■

»i

juo^?so ^^

i,V° {'" '■'

I, '•><» i'-^

°;»

0(0

.11 1^

I I

I. Emerald Green. 2. ChromousOxide. 3. Torre Verte.
Fig. 21.

trum to fall on a strip of a white surface, and that
from the other on a strip of the coloured surface
(see page 82). This is a more convenient method
than that just described, when the coloured surface
is small. The annexed figures (Figs. 19, 20, 21, 22)
show the results obtained from various pigments.

dbyGoogk

104 COLOUR MEASUREMENT AND MIXTURE.

From curves such as these we are able to produce
the colour of the pigment on the screen from the
spectrum itself. This is a useful proof of the truth
of the measurements made. To do this we must
mark off on a card (Fig. 23) the absolute scale of
the spectrum along the radius of a circle, and draw

too

lOOWhite

90
BO

^"^

"V,

^>^

.-'-

\--

...J

— -

^4-

*'..

-.,

....

^rt

/arf

■/-

,«

t>=

JO iO0| 7J'J ^^

^\^soS^ ?^V

j ^So ^i

)o 7

f" 7000'^^'^'^

IJ si

I. Indigo. t. Antwerp Blue. 3. Cobalt.

4. French Ultramarine*

Fig. 22.

Circles at the various points of the scale from its
centre. From the same centre we must draw lines
at angles to the fixed radius corresponding to the
various apertures of the sectors required at the
various points of the scale to measure the light

d by Google

COLOUR MEASUREMENT AND MIXTURE. 10$

reflected from a pigment. Where each radial line
cuts the circle drawn through the particular point
of the scale to which its angle has reference, gives
us points which joined give a curved figure. Such
a figure, when cut
out and rotated
in front of the
spectrum in the
proper position
(as for instance
by making the D
sodium line cor-
respond with that
on the scale), will
cut off exactly the
same proportion
of each colour
that the pigment
absorbs. The spectrum, when recombined, should
give a patch of the exact colour of that measured.
The spectrum must be made narrow, as the tem-
plate is only theoretically correct for a spectrum
of the width of a line, as can be readily seen.

Templates like these will always enable any
colour to be reproduced on the screen, and if the
light be used for the spectrum in which the colour
has to be viewed, be it sunlight, gaslight, starlight
— whatever light it is — the colour obtained will be

Prussian Blue
Fig. 23,

Method of obtaining a Colour
Template.

dbyGoOgk

I06 COLOUR MEASUREMENT AND MIXTURE.

that which the pigment would reflect if it were
viewed in that light.

The identity of the colour produced on the
screen by this plan with that measured, can be
readily seen by placing the latter in the reflected
beam of white light alongside the coloured patch
formed on the white surface.

Fig. 24.— Template of Carmine.

In Fig. 24 we have a mask or template of
carmine, which was used for determining if the
measurements were right. The black fingerlike-
looking space on the right was the amount of
red reflected light, and the other that of the blue

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 107

and violet ; scarcely any light at all was reflected
from the green part of the spectrum.

On page 108 we have given the diagram of the
luminosity of the spectrum in reference to a
standard white light. It will bring this luminosity
more home if, in a similar manner to that described
above, we make a template of this curve (fig. 25).

Offff/r YCICOW gSAHGS ',££it

Fig. 26.— Absorption of transmitted and reflected Light by Prussian
Blue and Carmine.

We can place a narrow slit horizontally in front
of the condensing lens of the optical lantern, and
throw an image of it on to the screen. If in
close contact with this slit we rotate the template,
we shall have on the screen a graduated strip of
white light, giving in black and white the apparent
luminosity of the spectrum as seen by the eye.

dbyGoogk

X08 COLOUR MEASUREMENT AND MIXTURE.

:i;;;;ib©

:::;;!!;;;;;; ;;;

WBl^'- :

^Bjlj^j^

dbyGoogk

COLOUR MEASWREMiENt AND MtXTURfe. 160

It has been stated in chapter V., that it is
generally immaterial whether a pigment is in con-
tact with the paper or away from it, so long as
the light passes through the pigment. The above
figure (Fig. 26) shows the truth of this assertion.
I. and II. are the curves taken of the light trans-'
mitted by Prussian blue and carmine respectively,
and III. and IV., from the light reflected from these
colours on paper.

To measure the difference in the intensities of
the rays of different sources
of light we can use a spec-
troscopic arrangement with
two slits (S) (Fig. 27) placed
« in a line at right angles to
the axis of the collimator.
One sHt is a little below the
other, the rays being reflected
to the collimating lens L.by ^-n^g-thfiS^^ofTo
means of two right-angled sources of Light.
prisms P, and two spectra are formed, one above
the other. By placing the rotating sectors in front
of one of the sources, the intensities of the different
parts of the spectrum can be equalized and measured.

The curves for the annexed figure (Fig. 28) were
derived from measures taken in this manner. If the
rays of a May-day sun are taken at lOO, it will be
seen what a rapid diminution there is in the green

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liO COLOUR MteASUREMENt ANt) MtXTtJRfi.

and the blue rays in gaslight. Gaslight onl
possesses about 20**/© of the green rays, whilst c
the violet hardly sVo- On the other hand th
light which comes to us from the sky shows a ver >
marked falling off in the yellow and red ray;^^-
A very easy experiment will convince us of th
difference in colour between skylight and gaslight

sJn dqht

— 1

ina

j»

(

^ JSJ

? U rS 14 13 12 ir 10 9 i

'> «

Fig. 28. — Spectmm Intensities of Sunlight, Gaslight, and Blue Sky.

If we let a beam of daylight fall on a sheet of
paper at the end of a blackened box, and cast
a shadow with a rod by such a beam, and then
bring a lighted candle or gas-flame so that it casts
another shadow of the rod alongside, one shadow
will be illuminated by the artificial light, and the
other by the daylight. The difference in colour
will be most marked : the blue of the latter light

dbyGoogk

COLOUR MEASURfiMENt AND MIXTURE. Ill

j^nd the yellow of the former being intensified
hy the contrast (see page 198).

By a little trouble the blue light from the sky

' may be compared with sunlight. A beam of light B

(Fig. 29) is reflected by

a silvered glass mirror
Jfrom the blue sky into
the box HH, at the end
of which is a screen E.
Another mirror A, which
is preferably of plain
glass, reflects light from
the sun on to a second
unsilvered mirror G
(shown in the figure as
a prism), which again
reflects it on to the
screen, and each of these

Fig. 29.— Comparison of Sun and
Sky Lights.

lights casts a shadow
from the rod D ; K are rotating sectors to diminish
the sunlight, and we can make two equally bright
shadows alongside one another. The bluer colour
of the sky will be very evident.

dbyGoogk

CHAPTER IX.

Colour Mixtures — Yellow Spot in the Eye — Comparison of
Different Lights— Simple Colours by mixing Simple
Colours — Yellow and Blue form White.

The colour of an object in nature, without ex-
ception we might almost say, is due, not to one
simple spectrum colour, or even to a mixture of
two or three of them, but to the whole of white
light, from which bands of colour are more or
less abstracted, the absorption taking place over
a considerable portion or portions of the spec-
trum. Notwithstanding this we shall now experi-
mentally show that every colour can be formed
by the simple admixture of not more than three
simple colours, if they be rightly chosen, and from
this we shall make a deduction regarding vision
itself. We are in a position to obtain three simple
colours by means of a slide containing three slits.
Now for our purpose we require that the three
slits can be placeid in any part of the spectrum,

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COLOUR MEASUREMENT AND MIXTURE. II3

and that they can be narrowed or widened at
pleasure. Instead of a card the writer uses a
metal slide, as shown in Fig. 30.

It will be seen that the three slits can be closed
or opened from the centre by a parallel motion.
They also slide in a couple of grooves, so that they
can be moved along the frame into any position.
The position they occupy is indicated by a scale
engraved on the front of the slide. Behind the

Fig. 3a— Slide with slits to be used in the Spectrum.

grooves in which the slits move are another pair of
grooves, into which small pieces of card CCCC
can slide, and thus close the apertures between the
slits. By this arrangement all rays except those
coming through the slits themselves are cut off. The
metal frame fits on to an outer wooden frame, which
slides in the grooves used with the card in the
apparatus as already described. It is convenient
always to keep the scale on the back of this wooden
slide in the same position as regards the shadow of

dbyGoogk

1 14 COLOUR MEASUREMENT AND MIXTURE.

the needle-point used for registering the position,
and to move the slits along their grooves when a
change in position is required. Using these three
slits three different colours can be thrown on the
same square patch on the screen.

A very crucial experiment is to see if we
can make white light by the admixture of three
colours, for if this can be done it almost follows
that any colour can be formed. We must use the
colour patch apparatus, and begin with placing one
slit in the violet near the line G, another between
E and F, and a third between B and C of the
solar spectrum, and fill up the gaps between them
with cards as shown in the figure. For our present
purpose it is better to make the colour patch and
the white patch touch each other, not using the rod,
as by this means we avoid fringes of colour. We
shall find that the aperture of the slits can be so
altered that we can produce a perfect match with
the white reflected light. By placing the rotating
sectors in front of the reflected beam we can
reduce its intensity, so that the two patches are
equally bright. By a tapering wedge we can
measure the width of the slits, and thus get the
proportions of these three different colours which
must be used to give the white. This is a sample
of the method that we employ when we match
any other jcolour. Suppose, for instance, it be

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COLOUR MEASUREMENT AND MIXTURE. II5

wished to measure the colour of a solution of
bichromate of potash; it is placed in the path
of the reflected light, and we have an orange
strip of light which we have to match. In this case
it will be found that the slit in the blue has to be
closed entirely, and only the .green and red slits
opened. The intensities of the two lights are
equalized by the rotating sectors as before. So
again with a solution of permanganate of potash.
In this instance no green light will be required
(or if any of it but a trifle), and the colour of the
permanganate will be formed by the rays coming
through the blue and red slits.

This plan is a very useful one for measuring all
kinds of transparent colours in terms of three rays.
The method of finding the intensity of any ray
of the spectrum transmitted by any such medium
has already been explained. . The latter has one
advantage over the former, in that the measure-
ments by it are exact, whatever source of light be
used to , form the spectrum. By the method now
described this is not the case. For instance, the
colour of permanganate of potash may be matched
in the electric light with the red and blue slits.
If the limelight were substituted for the electric
light, it would be found that the slits would require
other apertures, not proportional to those already
formed, to match the colour of this substance.

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Il6 COLOUR MEASUREMENT AND MIXTURE.

Fig. 31. — Screen

on which to

match Gamboge.

If we wish to register the tint of any pigment,
we have to slightly alter our mode of procedure.
Suppose, for instance, we wish to register the colour
of gamboge. In such a case we paint
a small bit of card (Fig. 31) with
the pigment, and divide the white
space on which the colour patches
are thrown into two parts, and cover
one-half with the pigmented card,
leaving the other half white. The
reflected beam illuminates the pigment, and the
spectrum patch the white. The widths of the
three slits are then altered till the two tints agree,
and the brightness matched by means of the
rotating sectors.

There are certain sad and aesthetic colours which
it might be considered cannot be matched by a
mixture of three colours. A brown colour, or "eau
de nil /' might appear to come out of the range of
matching. These colours, however, can be matched
in precisely the same manner as the brighter colours
are matched. Thus a brown pigment will be found
to require red and a little green, and a trifle of
blue; and the only difference between it and a
brighter shade of the same colour, is that more total
light has to be cut off" from it to give the sombre-
ness. A sad colour only means a pigment or dye
which reflects but little light, and if that be so it

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. II7

can naturally be matched by using but very small
quantities of the compounding colours.

There is one curious phenomenon to which
attention may be called in this matching, which is
worthy of remark. The match will be found to
differ according as the patches are compared from a
distance of a couple of feet, or from a considerable
distance. More green will be required in the latter
case than in the former. If matched at a distance
of about six feet, and the eyes be then turned
so that the edge of the patch falls on their
centres, it will be noticed that the colour mixture
appears of a green hue. This last experiment
indicates that the retina is not equally sensitive
for all colours throughout its area. Physiologists
tell us that what is known as the yellow spot
occupies a central position in the retina, and that
it absorbs a part of the spectrum lying in the
green. Now when the eyes are close to the patch,
its image occupies a considerable part of the retina,
and the colour is compounded as it were of the
colour as seen on the yellow spot, and of that
beyond it, for the yellow spot will take in an image of
from six to eight degrees in angular measurement.
When viewed at a distance we have the image of the
patch falling almost entirely on the yellow spot,
and hence a greater quantity of green is required,
as it has to make up the deficiency caused by the

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Il8 COLOUR MEASUREMENT AND MIXTURE.

absorption. When the eyes are turned a little on
one side the image falls on the outside of the
yellow spot, and the patch illuminated by the
mixed light appears green, compared with the
patch illuminated with the white reflected beam.
It is thus evident that when colour matches
have to be made, the distance of the eye from the
screen should always be stated, as also the dimen-
sions of the patches viewed. It may be fairly
asked why, if the half patch illuminated by the
mixed colours appears greener when the eye is
turned, the other should not equally do so. This
is a very fair question to ask. It must be re-
membered that one strip is illuminated with white
light, in which every coloured ray of light is com-
pounded, whilst in the other only three rays are
blended. The green ray chosen happens to be
taken from that part of the spectrum which is
absorbed by the yellow spot ; but all of the green
rays of the spectrum are not so much absorbed,
hence in ordinary white light, in which all the
green rays are present, only a small percentage
of the total green in the spectrum is absorbed,
compared with that absorbed from the single green
ray with which the match is made. No doubt both
patches are really greener when the eye receives
the impression, of their images outside the yellow
spot, but one is much greener than the other, and

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COLOUR MEASUREMENT AND MIXTURE. II9

it IS thus comparatively green. It is possible to
make a match with some colours with a blue-green
in which the phenomenon described does not ap-
pear ; but in cases where a match has to be made
with colours in which but little blue is required, it
would be impossible to make it, owing to the blue
existent in such a green-blue ray.

We will now return to our compounding of three
colours to make white. Why have we chosen the
positions of the slits which we did in the spectrum
for its formation? Would not other positions
answer as well } Let us give our answer by ex-
periment. Let us move the slit which is now in
the green towards the red ; we shall find that as
we do so — and keeping the blue slit of the same
width — that we shall have to close the red slit, and
alter the aperture of the green slit itself. If we
reason on this point we shall be forced to the con-
clusion that the green slit lets through more red
light of some description, as less red from the red
slit is required to make the match. If we move
the green slit almost into the yellowish green, we
shall find that the red slit has to be entirely
closed, and that white light is formed of the two
colours, yellowish green and violet. This shows
us that the yellowish green colour here used is
formed by a mixture of the red and green rays
which passed through the two slits in their original

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120 COLOUR MEASUREMENT AND MIXTURE.

positions. If we replace the slits in these positions
and close the violet slit, we are at once able to
verify it.

If we again form white light with the slits in
their original positions, and move the green sift
towards the blue, we shall find that, keeping the
red slit at a constant aperture, the blue slit will
have to be closed, and the green slit altered in
width. The necessity of lessening the aperture of
the blue slit shows that there is a certain amount
of blue light coming through the green slit At
one point, when the slit has travelled into the blue-
green, the blue slit may be entirely closed, and
white light be formed of this and the red, showing
that the blue-green colour is composed of the
same proportions of blue and green which passed
through the blue and green slits in their original
position. The positions chosen were arrived at by
the writer from experiments made in this manner,
moving first one slit and then the others, and the
position of the green slit was confirmed by a con-
sideration of the neutral point which exists in a
green colour-blind person's spectrum.

The method of mixing three colours together
gives us a means of imitating all kinds of white
light, as it does of coloured light. At page IIO
we have already given a diagram of the relative
amounts of spectrum colours in sunlight^ skylight

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COLOUR MEASUREMENT AND MIXTURE. 121

and gaslight. If we by any means throw a patch
of the light which we wish to match on the patch
formed by the colour patch apparatus, and interpose
the rod, we can measure the apertures of the three
slits, and thus arrive at the relative proportions of
each colour present. In an experiment carried
out, sunlight, the electric arc-light, and gaslight were
compared in this manner. The following are the
results, the red being near the C line, the green
near the E line, and the violet near the G line of
the solar spectrum.

Sun-
light.

Electric
Light.

Gas-
light.

Sky-
light.

Red

Green

Violet

100

193
228

100
203

250

100

95
27

100
760

Now from the above it might seem that as three
simple spectrum colours will give us the colour
of any pigment, that therefore two colours ought
to give us the same colour as any intermediate
simple colours in the spectrum which lie between
them; for instance, that the simple blue-green
ought to be obtained by mixing spectral green
and spectral violet together. This can be ascer-
tained with a single colour patch apparatus, by
cutting a slit in the card that fills up the aperture
between the two adjustable slits, and deflecting

dbyGoogk

122 COLOUR MEASUREMENT AND MIXTURE.

the beam transmitted through it by a right-angled
prism, and back on to the screen through another
similar prism, as described in chapter VIII. It is
more convenient, however, to use a duplicate appar-
atus precisely similar to the first, with the exception
that no collimator is required, placing them side by
side, and mirrors making the reflected beam from
the first traverse the second set of prisms. There
will be a reflected beam from the second apparatus,
which can be utilized in the same way as was that
from the first apparatus, and the two spectra will
vary together in brightness, as will also the new
reflected beam, since they all are formed by the
light coming through one slit. A patch of the
colour intermediate between the two is thrown on
the screen from the second apparatus, and the
second patch from the first apparatus overlaps it. A
rod placed in the usual manner throws two shadows,
which are illuminated by the two different beams.
If blue-green be a colour it is wished to match, it
will be found that no matter in what part of the
violet and green the slits are placed, no match can
be effected. But if some very small quantity of
red light be mixed with simple blue-green, that
then a colour identical in every respect as regards
the eye can be obtained from the violet and green
of the first apparatus. It must be remembered that
a mixture of red, green and violet form white, and

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COLOUR MEASUREMENT AND MIXTURE. I23

that they are mixed in definite proportions. No
matter how feeble in intensity the white may be,
the same proportions will still obtain. In the
above experiment, as the blue-green must contain
violet and green, the small quantity of red must
combine with the proper proportion of violet and
green, and will form white light, so that the match
is obtained by the residues of the violet and green
mixed with the small quantity of white light, of
which the red is the indicator.

We can test the truth of this argument in a very
simple way. If we add to the colour with which
the match has to be made a small quantity of
white light from the reflected beam, cutting oflf
more or less by the rotating sectors, we can get the
exact hue of the impure blue-green made by the
mixture of the colours coming through the two
slits ; and further we shall find that the amount of
white added corresponds with the amount of red
which would be required when the components of
the white light in the terms of the three colours
are taken into account. For spectrum colours
between the violet and the green it may therefore
safely be said that no match can be effected by
the mixture of violet and green light ; but that it
always gives the intermediate colour diluted with
white light. For colours between the green and
thq red of the spectrum,^ a very close, if indeed not

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124 COLOUR MEASUREMENT AND MIXTURE.

an exact match, can be made with the red and
green slits, without the addition of white.

If we take from the second apparatus light from
above the position of the violet slit in the firs
apparatus, that is, nearer the limit of visibility, i
will be found that a match is made, for at all events
a very considerable way with the violet slit alone,
by merely reducing the aperture, thus showing that
the colour is the same, only less intense. In the
same way it will be seen that the rays coming from
any point between the lower limit of the spectrum
to a little below the C line are identical in colour.

As we have arrived at the fact that in colour
mixtures of violet and green, white light is to b»
found in the colour produced, it follows that either
the violet or the green, or both, must themselves
contain some small proportion of white. It might
perhaps be said that violet is really a mixture of red
and blue, and hence the white in the mixture with
the green ; but if in the first apparatus we place
one slit in the purest blue we can find, and the
other in the red, and throw a violet patch on the
screen from the second apparatus, we shall be un-
able to form the same hue of violet by any means ;
it will always be diluted with white. Now as the
very blue we are using, if matched as above by
green and violet, requires white light to be added
to it, and as to match the violet with the same blue

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COLOUR MEASUREMENT AND MIXTURE. 12$

and red, white light has also to be added to it, it
follows that the violet must be freer from white
light at all events than the blue.
Jv There is one other experiment that must be
inentioned before leaving for a time this part of
our subject, viz. the formation of white by a mix-
ture of yellow and blue. If one of the slits be
placed in the yellow of the spectrum, a position will
be found in the blue where, if a second slit be
placed, and the apertures are adjusted, an absolute
match with the reflected white of the apparatus can
be secured. This experiment will be referred to later
on, when considering the question of primary colours.
i The above experiments have a great bearing on
the theory of colour vision, and should be considered
very carefully in connection with the shortened
spectrum which 'we have shown exists when red
colour-blind people are observing its luminosity.

There is one point to be recollected in relation to
the mixtures of the three or two different colours
which make white light. If different coloured pig-
ments be illuminated by the " made " white light,
they will not appear of the same hues, as a rule,
as when viewed by ordinary white light. They
will vary not only in colour, but in brightness.
This might be expected when the spectral light
which they reflect is taken into account.

dbyGoogk

CHAPTER X.

Extinction of Colour by White Light — Extinction of White
Light by Colour.

In the last chapter we have shown the impossi-
bility of matching the hue of the simple colours
between the violet and the green, unless a certain
and appreciable quantity of white light be added
to them. We will now turn to a phase of colour
measurement which will materially help us to see
why, in some cases, the addition of white light to
the simple spectrum colours, between the red and
green, does not appear necessary in order to make
a match with a mixture of red and green.

We will ask ourselves two questions: one fs,
whether any colour, and if so how much, can be
added to white without appearing to the eye ? and
the other, if any, and if so how much, white light
can be added to a colour without its- being
perceived ?

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COLOUR MEASUREMENT AND MIXTURE. 12/

Perhaps one of the readiest methods of explain-
ing exactly what we mean is by a rotating disc
Suppose we have a red disc, of nine or ten inches
in diameter, and at every one inch from the centre
paste on it a white wafer about one-eighth of an
inch in diameter, and cause it to rapidly rotate.
On examination we shall find that pink rings will
be formed by the combination of the white and
red near the centre, but that towards th6 margins
no rings will be visible, owing of course to more
red being combined with the same amount of
white. This shows that the eye is only sensitive
to a certain degree, and cannot distinguish a very
small diminution in colouiypin'fty. The m'teiiKfy
of the light has sometHj/fig to do with the number
of these piaVv' rings which are visible, as may
readily, Ve tested in a room. If the rotating disc
*^5eplaced near a window, and the number of rings
visible be counted, a different number will be
visible when it is placed in a dark comer. A
kindred experiment is to place red circular wafers
upon a white disc, and note the rings visible. This
gives the sensitiveness of the eye for the diminution
in intensity at the other end of the scale. It will
be found that there is a marked difference between
the two.

It is more instructive if we experiment with pure
colours, and so we must resort to our colour patch

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128 COLOUR MEASUREMENT AND MIXTURE.

apparatus described in Fig. 6. If a small circular
aperture about quarter of an inch in diameter be cut
in a card, and placed in front of the prism nearest
the camera lens (Fig. 32), the colour patch, instead
of being an image of the face of the prism, will be
an image of the circular hole,
and when the slit is passed
•through the spectrum we shall
have a coloured spot on the
screen, on which we can super-
pose a patch of white light from
the reflected beam. There are
two ways^inj^rh^ can re- ^^'^onTMsT" *"
duce tlie intensllJ^•■t7fv<^Je spot, by narrowing the
slit through which the^-^^al ray passes or
by placing the rotating sectoris i^_£ipnt of the
coloured beam. This last, perhaps, is tni^Yeadiest
plan, as it only involves the reading of the sec. ^-
V/e can then diminish the intensity of the coloured
spot to such a degree that by its dilution with
white light it will entirely disappear. It will be
found that red disappears at a different aperture
of sector to that required for the green, and the
green to that for the blue.

From our previous experiments in chapter VII.
we know the luminosity of the spectrum to the
eye, and it will be of interest to see what relation
the luminosity at which the spots of different

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. li^

colour disappear, when they are so diluted with
white light, bear to the total luminosity of these
rays.

In a set of measurements made it was found that
the reduced angular apertures required for the
colours indicated by the following were:
B required 300° * of aperture.
C „ 56° „

D „ 14' „

E „ 22'
F „ 150'
G „ 2100' ♦ „
The large numbers marked with an asterisk were
obtained by placing the rotating sectors in front of
the white reflected beam.

The light of D had to be reduced to 14* before

it was extinguished; therefore to extinguish the

Ipi^original light of this colour in the spectrum would

i trequire ^^, or I2'9 times the intensity of the white

ith
be
ire
he

II.

■he
on

ight of the reflected beam. With the E light it
ivould take ^, or 8*2 times the white light to ex-
inguish it, and so on. If we tabulate the results
n this manner, and take the white light necessary
:o extinguish the D light empirically as 98-5,
»rhich is its percentage luminosity in the spectrum
>f the electric light, we can then compare the
extinguishing factor with the luminosity in each

Dase.

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130 COLOUR MEASUREMENT AND MIXTURE.

Colour.

White requiked

TO EXTINGUISH

THE Spectrum.

White required
TO extinguish
THE Spectrum,

with 50 AS that
required at E.

Luminosity

Spectrum.

near line B

•6 ...

3'9 ...

4-9

c ...

D ...

3-2 ...

12*9

19-5 ...
78 ...

20-6

985

E ...

8-2 ...

F ...
G ...

V2
•087 ...

7-S •••
•56 ...

7-5
•6

The very close resemblance between the last two
columns indicates that the same luminosity of white
Hght is necessary to extinguish the same luminosity
of most colours, within the limits of observation that
is to say. Indeed the method of extinction was a
plan which Draper and Vierordt essayed, but the
results, tabulated from experiments made by them
with the apparatus they employed, give a curve
of intensity very unlike that given in Chapter VII.
In these experiments the luminosity of the orange
light corresponding to the D line coming through
the slit was measured, and it was found to be -155 of
the white light. Now according to the last table
but one iSo of this light was extinguished by the full
white light, consequently i| x 1^, or s of the orange
light was extinguished by the white light In
other words, if white light be sixty-two times

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. I31

brighter than the orange light, the colour of the
latter when the two are mixed will be invisible.
The extinction of all colours requires somewhat
more light than this, and a calculation shows that
the extinction of every colour is effected by white
light, which is seventy-five times brighter than the
colour. Artists are well aware that a pale wash of
a pigment may be washed over drawing paper, and
when dry is invisible to the eye. The above ex-
periments fully account for it.

The other experiment which was to be tried was
to see how much white light could be extinguished
by a colour. There are several ways by which this
can be effected. For instance we may superpose
a white dot on the colour^patch by placing a card,
in which a circular hole is cut, in the reflected beam
near the prism, from^which the reflection takes
place ; or by putting a black circular disc of small
dimensions pasted on a glass in the same position,
by which means the white light is superposed over .
the whole of the colour patch, with the exception
of what, when the colour is cut off, is a black spot ;
or again by placing a rod to shade half the patch
from the white light, but leaving the whole of it
exposed to the coloured beam. All these methods
have been tried, and it appears that the size of the
piece of the patch over which the white light is
thrown may have some effect on the resulting

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132 COLOUR MEASUREMENT AND MIXTURE.

curve, but of one thing there is evidence, viz. that
a great deal more white light can be mixed unper-
ceived with orange light, than can be with the green,
blue, or violet From one experiment it was found
that i part of white light of the same luminosity
as the orange could be mixed with the orange
and not be perceived ; but that with the green light
at E i would just be visible, whilst at F in the blue-
green the 1^ could be distinguished. Looking at
these results, and applying them in elucidating the
experiments in which it was attempted, but without
success, to match the intermediate colours between
violet and green (of which the light at F is a case
in point), by mixing them together, unless white
light were added to the simple colour; and the
success of the other experiment, in which orange
light could be obtained of the same hue as that at
D by a mixture of the red and green, it will be
noticed that 3*3 times more white light can be
added to the orange than to the green light at F,
without its perception. The white light produced
by the mixture in the first case might well show
when mixed with the green, but might pass wholly
unperceived when mixed with the orange.

dbyGoogk

CHAPTER XI.

Primary Colours — Molecular Swings — Colour Sensations —
Sensations absent in the Colour-blind.

For some purposes it is advantageous to show
experiments before indicating the deductions from
them which may lead to a theory. Those described
in Chapter IX. will enable us to treat the theory
of colour perception from a standpoint of some
advantage. How is it that the combination of
three colours suffices to form white, or to match
any colours we wish, be they spectrum colours
to which a little white is added, or the colours of
pigments ? The most plausible theory that can be
advanced is that it is only necessary for the eye
to be furnished with a three-colour-perceiving
apparatus to give the impression of every colour,
and yet this would be somewhat difficult to
believe had we not had the experiments narrated
in that chapter before us. We should have almost

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134 COLOUR MEASUREMENT AND MIXTURE.

expected some machinery in the eye to exist, which
would answer to the rhythmic swing of the rays of
every wave-length which together make up white
light. But now we have to stand face to face
with the results of experiment, and we find that at
the most only three colours are necessary to make
up white light, and that from these three spectrum
colours we can form any others, with the limitation
already mentioned, when some simple colours are
in question.

We must here digress for a moment, and notice
the fact that from our experiments we have derived
the three primary colours as they are called, viz. red,
violet, and green ; the definition of a primary colour
being that it cannot be formed by the mixture of
any other colours. We have ascertained that yellow
and blue make white. It is therefore evident that
blue, yellow, and red cannot be primary colours,
since two of them form white ; and we have more-
over shown that yellow can be made from green
and red ; hence it might be fair to assume that the
three primary colours are red, green, and blue.
But blue, when mixed with a very small percentage
of white light, can be made by green and violet.
Hence, in the white light formed by the two colours
yellow and blue, we have the first made by green
and red, and the second by green and violet;
hence the three colours which really make the white

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COLOUR MEASUREMENT AND MIXTURE. 13$

light are red, green, and violet. The approximate
positions of these three colours in the spectrum
are those already indicated ; though, as we shall
presently see, it is highly improbable that any per-
son whose eyes are what are called normal, has
ever experienced the fundamental green sensation.

The fact that red, yellow, and blue cannot be
primary colours has been mentioned, as even now
it is sometimes taught that they are so. As
long as the theory of colour principally lay with
artists there was reasonable ground for their as-
sumption, since they worked with impure colours,
viz. those of pigments ; and as we shall see later on
the truth of the assumption agreed with such ex-
periments as they would make. When, however,
the question was taken up by the physicist with
more exact methods of experimenting, and with
pure colours, the falsity of the old triad was soon
capable of proof.

To return from our digression : how it is that
three mixed colours can give the sensation of white
light is at first sight hard to understand ; but a
reference to the action of light on a photographic
salt helps us in some degree. In the case of a
sensitive salt, such as the bromo-iodide of silver,
we find that a chemical decomposition is caused
by the violet end of the spectrum, and is only
feebly affected by any other part, though with

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136 COLOUR MEASUREMENT AND MIXTURE.

prolonged exposure even the red will cause it The
annexed figure (Fig. 33) gives the idea of the relative
action of different parts of this violet portion.

ioo

M
.80

80
60
^0
30

■■■

■■■■■■■■■■■
■■■■■■

■■■■■■■■BaH

A^tBfl.
Fig. 33.— Curve of Sensitiveness of Silver Bromo-iodide.

The height of the curve shows the relative effects
produced. * Now this curve is not symmetrical, but
has a maximum effect nearer to th« violet end of
the spectrum than to the red. The atomic com-
position of the silver bromo-iodide is probably two
atoms of silver and one of bromine and one of
iodine oscillating together, and we can conceive of

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 1 37

some one atom, the period of whose swings in
its molecule is isochronous with some wave-length
of light. Further, we can conceive that, like
a pendulum whose vibrations are increased in
magnitude by well-timed blows, the swing of
the atom is also increased, and that eventually it
gets beyond the sphere of the attraction of its
parent molecule, leaves it, and is attracted to
some neighbouring molecule of different con-
stitution, and that thus a chemical change is in-
duced. This we can conceive, but how can other
waves, which are not isochronous with the rhythmic
swing of the atoms, alter the composition of the
molecule? If we have an impulse given to a
pendulum exactly timed with the period of oscilla-
tion, there is no doubt that the swing is increased. If
we have one nearly in accord, it will be found that
though the swings are not increased in amplitude
so greatly as when there is perfect accord, yet an
increased swing is given, and as exact accord is
removed further and further, so the increase in
the swing of the pendulum gets smaller and
smaller. In somewhat the same manner it is
possible that many series of waves, differing in
wave-length, and therefore in periods of oscillation,
may be capable of increasing the amplitude of a
swing, and with the photographic salt this probably
occurs, with the result which we see in the above

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138 COLOUR MEASUREMENT AND MIXTURE.

figure. Suppose in the eye we have three such
sensitive pendulums which are capable of respond-
ing to the beats of waves of light, it requires
. no great imagination to see that one such pen-
dulum will respond not only to that wave of
light which is isochronous with it, but also with
waves shorter and longer than that particular
wave. The same pendulum indeed may respond
to the whole of the visible spectrum, but when far
off from the maximum the response would be
very small indeed. We may therefore assume that
though each pendulum may have its maximum
increase of oscillation at one part of the spectrum,
yet at other parts not only it alone answers to the
beating of the waves, but that the other pendulums
are also affected by the same, and thus the whole
spectrum is recognized by the swings more or less
long, of either one, two, or of all three.

To Thomas Young is usually attributed the
three-colour theory, though it seems to have been
promulgated in an incomplete state some time
before; Clark-Maxwell and Helmholtz revived it
in later years, and it is usually known as the
Young-Helmholtz theory. It should be remarked
that the three fundamental colour sensations are
not of necessity the same sensations as are given
by the three primary colours, as we shall see further
on. The following figure (Fig. 34) is taken from.

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COLOUR MEASUREMENT AND MIXTURE. 1 39

Helmholtz's physiological optics, as diagrammatic
of the three sensations.

To this diagram there is an objection, in one
respect, viz. that it gives the
same luminosity-value to the
blue of the spectrum as it does
to the red and green. It has
been seen that if we call the
luminosity of the yellow lOO,
that of the blue is about 5.
The objection does not hold
if it is remembered that the
three maxima of impressions
are taken as equal. If the
ordinates were increased, so
that the maxima were of the
same height as that of the
photographic curve, the resemb-
lance between them and this
last would be very marked. It
will be noticed that each of the
three colour sensations is not
only excited by a limited por-
tion of the spectrum, but by
all of it, the height of the
curves being a measure of th^ir
response.

Now assuming that this is the case, since a'

dbyGoogk

I40 COLOUR MEASUREMENT AND MIXTURE.

certain d^^ree of stimulation given simultaneously
to the three sensations causes an integral sensation
of white light, it follows that the colour perceived
in every part of the spectrum is due to the excess
of stimulation of either one or two of the funda-
mental sensations, together with the sensation of
white light. If this diagram were correct, at no
point in the spectrum is one fundamental sensation
excited alone, but we believe that the diagram
obtained by Koenig (Fig. 35), from colour equa-
tions (which will be explained in our next chapter),
is more exact, and that it is probable that in the
extreme violet and extreme red of the spectrum
the only sensations which are stimulated are the
violet and red respectively. Our measures in the
red and violet of the spectrum make it appear
that each of the two sensations can be per-
ceived unaccompanied by any others, and the
fact that the red colour blind person perceives a
shortened spectrum in the red end, is a further
proof of this deduction, so far as the red is
concerned.

The colour which the fundamental green sensa-
tion excites in the normal eye has probably never
been seen, nor can be seen. This is due to the fact
that all three sensations overlap in the green ; that
is, that the pendulum which answers to the green
colour in the spectrum also affects, but with much

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. I4I

less energy, the other two pendulums, which
respond to the red and violet sensations.

The word pendulum has been used advisedly,
for it may equally as well apply to a molecular
aggregation as to one which is visible and measur-
able. Without entering into the physiological
structure of the eye, we may say that it has usually
been assumed that the pendulums are the ends of
nerves which vibrate with the waves of light ; but
this seems rather doubtful. Gross matter, such as
these ends are, compared with the molecules of which
they are built up, cannot, as a rule, vibrate with waves
of light, and there seems to be no reason why there
should be an exception in the case of the eye. It
seems much more probable that a chemical decom-
position takes place in some substance attached to
them, and where such decomposition takes place
electricity of some kind must be produced. In
other sensations of the body the nerves act as
telegraph wires, carrying messages to the brain,
and it is not improbable that the nerves of the
eye are employed in somewhat the same manner.
Professor Dewar has shown that when light acts on
an extirpated eye, a current of electricity does
traverse the nerves, and of such an amount that it
can be shown to a large audience. This experi-
ment is not, however, conclusive, as the effect may
be mistaken for the cause. This idea, however,

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142 COLOUR MEASUREMENT AND MIXTURE.

is only hypothetical, as is indeed the hypothesis of
the mechanical action of light on the gross matter
of which the rods and cones attached to the retina
'are composed.

We have in a previous chapter stated that there
are some eyes in which the sensation of some
colour is altogether absent, and in others in which
it is more or less deficient. Thus some eyes appear
to be lacking wholly in the sensation of red, others of
green, and some very few of violet ; and there have
been cases known in which two sensations, the red
and violet, have been totally absent. In the first
case, where the sensation of red is entirely absent,
what is known to the normal-eyed as white can be
matched with a mixture of blue and green, and
there is a place in the spectrum that is recognized
as white. Similarly white can be matched by a
green blind person with a mixture of red and
blue.

To those who may be curious to see the colour
which red and green blind persons would call
white, a very simple means is at hand to demon-
strate it Using the colour patch apparatus with
the three slits inserted in tfie slide, and in the
positions we have indicated in the violet, green,
and red, and forming white light for ourselves on
the screen, if we cover up the red slit entirely we
shall have a patch of sea-green colour, which a red

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. I43

blind person would call white ; and if we cover
the green slit, uncovering of course the red, we
shall have a brilliant purple, which to a green blind
person would be white. They both would call
white what the normal-eyed person sees as white,
for the simple reason that either the red or the
green mixed with the remaining colours would be
unperceived. The examination of colour-blind
people is of prime importance for testing any
theory of colour vision. For instance, if it were
asserted that the fundamental sensations did not
overlap as shown in the diagram above, then it
would follow that at some place in the spectrum
there would be a dark point. If they do over-
lap, it must follow that both for the red and for
the green colour blind person there must be some
place in the spectrum where what is white light to
them is produced.

Colour-blind people were tested with the colour
apparatus. The reflected beam and the colour
patch were made to cast shadows as before, and the
rotating sectors placed in the path of the former.
A slide with one slit was passed across the spectrum,
and the position noted where it was said that the
two shadows were illuminated with white light ; to
the normal-eyed person one shadow of course
appeared illuminated with the sea-green colour, or
bluish green, according as the observer was red or

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144 COLOUR MEASUREMENT AND MIXTURE.

green colour blind. The ray in the spectrum
which to the red colour blind is white, has a wave-
length of about 4900, and that for the green colour
blind a wave-length of 5020, which corresponds to
the position in which we usually place the green
slit when a normal-eyed person is making colour
matches.

It may be further remarked, that if the maxima
of all the three colour sensations are taken, as in the
diagram, as of equal value, that the place in the
spectrum where the white light is perceived by the
colour-blind is where the two sensations are of
equal strength, that is, where the two curves cut
one another, and are of equal height By obtaining
the proportions of the different colours with colour-
blind persons which make up what to them is
white light, the curves for the two sensations can
be worked out in the form of simple equations.

The experiments carried out with colour-blind
people are of the most interesting character, and a
good deal remains to be done with the data already
obtained from them.

To the popular mind a colour-blind person is
usually thought a strange creature, and it is a
matter of wonderment, if not of amusement, that
they cannot distinguish between the red of cherries
and the leaves of the cherry tree. The physicist,
studying the theory of colour, views the matter quite

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 145

differently, and he looks upon an intelligent observer
of this class as a boon. It may be remarked that
both the red-blind and the green-blind persons
would be unable to distinguish between the cherries
and the leaves. The red-blind person would see
the cherries as green, as also the leaves ; whilst the
green-blind person would see both as red. Without
regarding form it is probable that the red- blind
would see the leaves as a bright green, whilst the
green-blind would see them as darker red than the
cherries. Failure to distinguish between the two is
more likely to occur with the green of leaves, and
the red of such fruits as cherries, since the former
contains a marked proportion of red in it, and the
latter a small proportion of green.

One highly-educated gentleman was led to know
his deficiency in colour sense, by hearing a com-
panion on a tour going into raptures over a sun-
set. He saw but little difference between it and
that to be seen at midday. Testing his vision
it appeared that he was totally blind to the sensa-
tion of green, and that white and purple would con-
sequently be mistaken by him for one another.
The crimson on the clouds, illuminated by the set-
ting sun, would appear to him as only slightly
different to the white clouds which he would see
at midday; in fact he would be always seeing
what to us would be a sunset. For this gentleman

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146 COLOUR MEASUREMENT AND MIXTURE.

to mix spectrum colours to match others would
evidently be no guide to normal-eyed persons.

We believe that amongst us in our daily life
we have many persons who are blind to some
colour, but who are not aware of it, or if they are
aware of it, hide their defect as far as possible.
That some are igjnorant of it to a late period of
their life we know.

We have said that there are cases in which persons
are only defective in colour perceptions, and not
wanting in them altogether. The former are more
common than the latter, and to the experimenter
are by no means so interesting. They are only
alluded to here to indicate that there are degrees
in the defectiveness of eyes to colour. One point
which must be remembered here is that all colour
production for registration by the mixture of three
colours is delusive, unless the eye of the operator is
tested for its colour sense.

dbyGoogk

CHAPTER XII.

Formation of Colour Equations — Koenig's Curves — Max-
well's Apparatus and Curves.

The plan of obtaining colour equations will by
this time have become fairly evident. And we may
as well illustrate it by equations obtained with the
apparatus we have been using in our previous ex-
periments. Let us suppose we have an individual
who is desirous of having his eye-sight for colour
tested, and that we have the slide with the three
slits in situ. It will be found that when we alter
their width and form white light with them, match-
ing in purity the white light of the reflected beam,
that we shall have to reduce the intensity of the
latter very considerably, by means of the rotating
sectors. The aperture may sometimes be as- small
as 4^ and at other times perhaps somewhere be-
tween 4** and 5^ Now the variation ij
between 4^ and say 47, is very co^^^|^a^e,^t
it is highly probable that the Utter, tsx^^he

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148 COLOUR MEASUREMENT AND MIXTURE.

estimated as 4*6, since only degrees are marked
on the sectors. It therefore becomes essential
to use a less brilliant reflected beam for the com-
parison, and this is secured by using as a mirror a
plain unsilvered glass. What before read 4 will
perhaps read 60, and 47 will be 70!^, whilst 4*6
would be 69, a difference easily read. We can
now commence operations. Let us then place the
red slit at say (35) of the scale, the green at (28),
and the violet at (17), and make white light of the
same intensity by altering the apertures of the slits.
Let us do the same with the slits at (34), (28), and
(17), instead of at (35), (28), and (17); and again
make white light, and similarly with the slits at (35),
(28), and (18) ; and let the following be the results —
(i) 20(35) + 60(28) + 40(17) = 100 W

(2) 10(34) + 55(28) + 40(17) - 100 W

(3) 20(35) + 59(28) + 10(18) = 100 W
Subtracting (i) from (2) we get —

10(34) = 2o(3s) + 5(28)
or (34) = 2(35) + 1(28)
which means that the colour sensation at (34) is
made up of two parts of the sensation of (35),
together with J part of the sensation of (28).

In the same way we find that the colour sensation
of (18) is made up of the sensations of (17) and (28).
(18) = 4(17) + ^V(28).

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COLOUR MEASUREMENT AND MIXTURE. I49

In this way all the different colour sensations
can be referred to the sensations which we may
happen to consider as best representing the funda-
mental sensations. What these are is a matter still
unsettled ; though from the equations formed by
colour-blind people, who only require really two
colours to form equations, their places are approxi-
mately known ; evidently as before said, the ray
in the spectrum which the green colour-blind per-
son sees as white light, is that where to the normal
eye the green fundamental sensation is purest,
being free from predominance of either of the
other two sensations, and might be taken as a
standard colour. Now if our luminosity curve is
correct, and if the sum of the luminosities of each
colour separately is equal to the luminosity of the
colours when mixed (which we have shown to be
the case in chapter VII.), it follows that the correct-
ness of the measures can be checked by using the
widths of the slits as multipliers of the luminosities.
These luminosities can then be added together, and
they should equal in luminosity the white light
with which the comparison was made. The results
can be compared together by reducing the equations
to the same standard of white light.

The following is a set of observations which bear
this out.

The red and violet slits in this case were kept at

dbyGoogk

ISO COLOUR MEASUREMENT AND MIXTURE.

35 and 17*8 on the scale, and the position of the
green slit altered.

Position of Slits.

Aperturb of

Suts.

Luminosity of
Colour.

Sum of the
Luminosity of
EACH Colour
multiplied by
THE Aperture.

R
35

R
"5

V
112

R
181

•65

28-5

17-8

4930
4989

280

17-8

119

100

181

61 5

•65

2775

'7*S

122

181

•65

4960

2735

'7*2

181

*^5

4907

27-0

'7'S

181

33*2

•65

4954

26-3

17-8

133

125

181

203

•65

260

17-8

134

ISO

181

167

•65

4952

25-85

17-8

135

170

181

150

•65

4993

Mean 4959

The red slit was at a point in the spectrum
between C and the red lithium line, and excited
probably the fundamental sensation of red alone.
The violet slit was close to G, and probably in this
case the fundamental sensation of violet was almost
excited alone. With the green slit the reverse was
the case, all three fundamental sensations being
excited. At 26*3 the green sensation was probably
the fundamental sensation mixed with white light
alone, as at that point the green blind person saw
white light in the spectrum, on the red side of it
there being what he describes as a warm colour,
and on the violet side a cold colour.

An inspection of the table will show how very
closely the sum of the luminosities agree amongst

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 15I

themselves, the white light formed by them in each
case being of equal intensities. It must be recol-
lected that white light is not necessary to form
colour equations ; colours may be mixed to form
any other colour, which may be taken as a standard.
This is often useful in the case of the light between
the violet and the blue, where the luminosities are
small compared with the luminosity in the green,
yellow, and red.

Fig. 35. — Koenig's Curves of Colour Sensations.

By taking a large number of colour equations,
Koenig, who works in Helmholtz's laboratory, has
derived what he considers curves of the three
fundamental sensations in a normal-eyed person,
and also those of the colour-^blind. It may be said
that with the colour-blind only two of the funda-
mental sensations are seen, and therefore only two

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152 COLOUR MEASUREMENT AND MIXTURE,

I ; 111!

curves are found, and that these agree in the main

with some two of the curves of the three belonging

to the normal-eyed.

Maxwell was the first to
make a definite piece of ap-
paratus for the purpose of ob-
taining colour equations, and
we reproduce from his paper in
the Philosophical Transactions
of the Royal Society for 1 8 — ^
a somewhat modified diagram
of it.

This apparatus is often known
as Maxwell's colour-box, and is
in fact a spectroscope reversed.
With a collimator and prisms
we form a spectrum on the
focussing-screen of the caniera
(Fig. 6), by light coming through
the slit, and we can obtain light
on the distant screen, a patch of
any colour, by placing in the
spectrum slits as given at Fig.
30. If we were to illuminate
the slits so placed with white
light, and look through the slit
of the collimator, we should see

the front surface of the first prism illuminated by

III

^\Q. 36.
Maxwell's Colour-box.

dbyGoOgk

COLOUR MEASUREMENT AND MIXTURE. 1 53

the mixture of the colours which would, when the
light illuminated the collimator slit, have formed
one colour patch on the screen. In Maxwell's
apparatus, the slits" Si, Sj, S, are illuminated by the
light reflected from a white card C, placed in the
sunshine, the rays passing through them fall on two
prisms Pi, Pa, are reflected back again through these
prisms by a concave mirror Mg, are received on
another mirror M, and fall at E on to the eye. At
A is an aperture in the box, letting through white
light onto a mirror Mi, which reflects it through a
lens L on to Ma, which again reflects it on to M,
and so to the eye at E. Thus at E an image of the
prisms, and an image of the aperture are seen, and
the white light of the latter can be compared with
the mixture of the colours formed by the prism
passing through Si, S2, and S3.

Suppose we have one slit Si, the white light will
be decomposed by the prisms, and will be seen at
£ as light of the same colour as would be seen at
Si, if the light were sent from E to Si, and so with
the other slits. Thus when two or three of the
slits are uncovered, the light falling on the eye at
E will be a mixture of two or three colours.

There are two drawbacks to the mode of illumin-
ation used, one being that the quality of sunlight
varies, and therefore colour equations will not be
accurately comparable one with the other; and

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154 COLOUR MEASUREMENT AND MIXTURE.

the second is that the light reflected from the card
is not absolutely the same in all directions, and it
cannot be perpendicularly placed to each of the
rays which strike the prisms, after passing through
the different slits. This latter is a small objection,
and is not of much account, but the first drawback
is a more serious one.

Fig. 37.— MaxweU's Curves of Colour Sensations.

With this apparatus, then. Maxwell formed
his colour equations, but he fixed as the colours
which may be called his standard colours, portions
of the spectrum which are certainly not pure, and
hence he got curves which are net as perfect as
those of Koenig.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 155

It will be seen, for instance, that his red and
violet curves do not overlap, but touch each other
near E. Were this true, the green colour-blind
person should see a dark space in the spectrum,
since the green sensation is missing in such eyes.
As a matter of fact the luminosity of the spectrum
is very considerable to such a person at this point

It will also be seen that some of his curves are
negative curves lying below the base. This shows
that the three standard colours he took are some-
what wrong. The dotted curve gives the com-
bination of his three sensations at every point, and
should be the luminosity curve ; but owing to his
having taken empirically certain standards of lumin-
osity for his three colours, it does not represent the
truth, as may be seen on comparison with Fig. 11,
page 78.

It must be recollected that since Maxwell's
observations the subject has been largely experi-
mented upon, and naturally improved appliances
and greater knowledge have enabled more nearly
correct views to be entertained regarding it

dbyGoogk

CHAPTER XIII.

Match of Compound Colours with Simple Colours — All
Colours reduced to Numbers — Method of matching a
Colour with a Spectrum Colour and White Light.

If we place the solution of bichromate of potas-
sium in front of the slit of the collimator, we shall
see that on producing a spectrum on the screen, all
rays from the red to the yellow-green pass ; hence
bichromate of potash transmits a colour which is a
compound colour.

It has been shown that this orange colour and
the spectral yellow can be matched by mixing the
simple colours of red and green together ; but it
will be instructive to see if a simple colour in the
spectrum itself can be found which can match such
a compound colour as that of the bichromate.

If we place the bichromate in the reflected beam
of the colour patch apparatus and illuminate one
shadow cast by the rod with the light trans-
mitted by it, and pass a slit along the spectrum, to

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 1 57

produce monochromatic light, with which the other
shadow of the rod is illuminated, a position will be
found near the orange sodium line " D/' where the
two colours apparently match in every respect;
when the intensities of the two illuminated shadows
are equalized as before by the rotating sectors. In
the same way by filling the part of the square
with the pigment on which the shadow illuminated
by the reflected beam falls, we can see if we can
match emerald green, cyanine blue, and other
coloured pigments.

It will often be — more often than not — necessary,
however, to dilute the spectrum colour thrown on
the white half of the patch with a trace of white
light By reference to our previous experiments we
arrive at what may appear an unlooked-for result,
that no matter what the colour may be, wie can refer
it to one ray of the spectrum, together with a per-
centage of added white light. It is worthy of
remark, that the place in the spectrum where the
simple and the compound colours match, varies
according to the kind of light with which the pig-
ment is illuminated. This we can show in a very
simple way.

To persons who are totally colour-blind to one
sensation, viz. the green or the red, the matching
of a compound colour with a simple one in the
spectrum should possess no difficulties. Takings

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158 COLOUR MEASUREMENT AND MIXTURE.

the trichromic theory of three sensations for the
normal-eyed person, it is evident that only the
following classes of sensations are possible in the
normal-eyed, the green colour-blind and the red
colour-blind —

Nonnal-eye.

Green colour-blind. Red colour-blind.

ivec • • • • • •

Red

• •• • "^^

Green •••

—

... Green.

Violet

... Violet

Mixtures of red

—

• •• ""^

and green

Mixtures of red

Mixtures of red —

and violet

Mixtures of green

•••

... Mixturesofgreen

and violet

and violet.

Mixtures of red,

•••

••• ""•

green and

violet

If we take as a type of colour-blindness the
green colour-blind person, we see that every colour
in the spectrum must be either pure red or violet,
or else these colours mixed with more or lees white
light, since these two sensations when excited in
certain proportions give the sensation of white. At
one place, which is commonly called the neutral
point, the proportions of the two colours are such
that the impression there given is only white; hence

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COLOUR MEASUREMENT AND MIXTURE. 1 59

it follows that, between this neutral point and each
end of the spectrum, the rays are mixtures of
violet and white, or red and white, the dilution of
the colours varying from no white to all white. As
every compound colour must be a mixture of the
same two colours in certain proportions, it follows
that the green colour-blind person can match every
compound colour with some one ray of the spec-
trum, and that every colour must to him be either
red or violet, diluted with different proportions of
white light.

In the same way, a person who is colour-blind
to the red can also match any colour with a single
spectrum colour, and he will see it as green or
violet diluted with more or less white light. This
can be readily understood, but it is not quite so
plain how any colour sensation felt by the normal
eye can be referred to the spectrum.

If we take three rays in the spectrum — one in
the red between C and the red Lithium line which
we will call if, another in the green between F and
b which we will call G, and a third in the violet
near G but on the H side of it, and which we may
call V — then by varying their intensities (which is
equivalent to varying the luminosities) and mixing
them, we can give the same impression to the eye
that any compound colour gives ; and that any inter-
mediate simple spectrum colour gives, if very slightly

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l6o COLOUR MEASUREMENT AND MIXTURE.

diluted with white hght With these same three
colours, but in different proportions, we can a'^^o
give the impression of white light to the eye. The.
intermediate spectrum colours between the green
and the violet rays selected when slightly diluted
are imitated by mixing these rays together in
different proportions, and similarly those lying
between the red and the green by mixing together
these rays in different proportions — and there is
some ray present in the spectrum which, when
very slightly diluted with white light, has the same
colorific effect on the eye as the mixtures of the
pairs V and by and G and i?, in any proportions
whatever.

Let the luminosities of the rays R G and F,
which give the impression of white light, be a^ b
and c units respectively, and /, q and r those which
give that of the colour which has to be registered
and reproduced. We then get the following equa-
tions — where W is white, w its luminosity, Z the
colour, and z its luminosity —

aR + bG-^- cV^wW—(i.);
pR + qG + rV^ zZ— (ii.) ;

Then evidently —

{a '\- b '\' d)=^w\ and (p + g + r)= z.

Let p = aa, g = fi b, r==yc,
Then we may write (ii.) as—

aaR + fibG + ycV zZ — Qil).

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COLOUR MEASUREMENT AND MIXTURE^ l6l

Now either a, p or y must be smaller than the
o^er two. As an example, if a be the smallest, we
multiply (i.) by a when we get —

aaR + adG + acV=awW — (iv.)

Subtracting (iv.) from (iii.) and we get —
ifi — a)bG + {y — a)cV=^zZ — awW.
Now it has already been stated that between V
and G there is some ray which gives the same
sensation of colour, mixed with a very small quan-
tity of white light, as the above mixture of V and
G — let us call it X and its luminosity x \x being
evidently equal to (fi — a) b + (y — a) c\ and \i the
luminosity of the small quantity of white added.

We then get zZ = xX + (/x + a) W.

Here we have the colour Z in terms of a single
ray, and of white light.

This same holds good when in (ii.) y is smaller
than a and )3; but it does not do so should it
happen that )3 is the smallest, for there is no part
of the spectrum which contains simple colours
giving the same sensation to the eye as mixtures
of red and blue. There is, however, a very simple
way in which the registration of such a colour (which
it must be remarked must be of a purple tone) can
be effected. It can be fixed by its complementary.
To do this we must add to (li.) a certain amount
of R and V, which will make the whole white.
Thus, suppose in (iii.) a to be larger than y and y

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1 62 COLOUR MEASUREMENT AND MIXTURE.

than j3, then we must ad'd <I>6G + OcV and we
have

aaR + {p + (l>)iG + {y+e)cV=nW=Z+(l>bG + ecV;
but ()3 + <^), and (y + 0) each equal a .' . n = aw.
.-. Z + (f>dG + ecV=awW.

Now between V and G^ in the spectrum there is
some single colour which gives the sensation of the
mixture of G and V. Let it be X^ with luminosity
x\ together with white whose luminosity is jut',
which must equal (^ 6 + c),

.-. Z+x,X' + iJ W=awW
Z=(aze/-/i') W'-x' X^

which again is the colour expressed in terms of
white light less the complementary colour. We
have thus arrived at the very simple deduction that
the hue and luminosity of any colour, however
compounded, may be registered by a reference to
white light and a single ray of the spectrum.

In practice this dominant ray is very easy to
find. Suppose we wish to determine numerically
the colour of a signal-green glass in the electric
light, we should proceed as follows —

The colour patch apparatus (described in chapter
IV.) is employed, and the coloured glass is placed
between the silvered mirror which reflects the
beam already reflected from the first surface of
the first prism of the spectrum apparatus, and the

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COLOUR MEASUREMENT AND MIXTURE. 163

screen, and a square image of that surface of the
prism showing the tint of the glass is formed on
the screen by means of the lens. Touching this
image is a square patch of white light formed by
the re-combination of the spectrum by means of
another lens. An opaque slide containing an ad-
justable slit is moved across the spectrum in the
manner described in the chapter referred to until
the colour of this last patch is approximately the
same hue as that of the glass.

In the path of the reflected beam, but between
the prism and the silvered mirror, is inserted a piece
of plain glass which can be made to reflect part of
the beam into the spectrum patch of light, a square
patch of the white light being formed by means of
a third lens. We thus have monochromatic light
mixed with white light. The requisite intensity of
the added white light can be adjusted by means of
the rotating sectors, as described in the same
chapter, which open and close at will during rota-
tion, and the total luminosity of the mixed beams
can be altered by this, together with the adjustable
slit in the slide. The slit may probably have to be
moved in the spectrum to make the hue of these
mixed lights the same as that of the glass, but by
trial the position of the ray whose colour wljen
diluted with white makes the match is readily found.
The position of the slit in the spectrum is noted, as

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l64 COLOUR MEASUREMENT AND MIXTURE.

also the aperture of the sectors. The relative lumiii'
osities of the beam reflected from the plain glass
mirror and of the coloured ray is next measured by
placing a rod in the path of the two beams, and
equalizing by the sectors the luminosity of the
shadows which are illuminated, the one by the
spectral ray, and the other by the white light.
When the sector aperture is noted the registration
is complete, as far as hue is concerned, but the
luminosity of the ray transmitted through the glass
should be compared with that of the reflected
beam, and then the luminosity is also recorded.

Should the colour of a pigment be in question,
the ray reflected from the silvered mirror is made
to fall on the pigmented surface and the same
procedure adopted.

If a purple glass (say) has to be registered, we
proceed in a slightly different manner. The patch
of coloured light passing through the purple glass
is superposed over the spectrum patch, and the slit
in the slide is moved till a ray is found which will
make white light when superposed on the colour
of the glass. The luminosities of this white light,
of the reflected beam, and of the spectral colour
are compared "inter se," and there are then
sufficient data with which to make numerical
registration.

Coloured glasses to be used at night with oil or

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COLOUR MEASUREMENT AND MIXTURE. l6S

gas, or pigments to be viewed by these lights, must
be registered in these lights. As the spectrum
colours are always the same, it is convenient to use
the electric light spectrum, and the only alteration
in the apparatus is to use two gas-lights to illumin-
ate two square apertures, in front of one of which
the glass whose colour has to be measured is
placed. The images of these apertures are thrown
on the screen, the coloured image touching the
square image of the spectral colour patch, and
the naked image over the latter. The same
determinations are gone through as those just
described.

The following are the determinations of some
glasses —

Glasses
Measured.

Wave-

lengths of

Dominant

Ray.

Percentage

OF W^hite

Light.

Percentage
OF Luminos-
ity OF Light

TRANSMITI'ED
THROUGH

THE Glass.

Ruby
Canary
Bottle Green

6220

5850
5510

2
26
31

131
82-0
io*6

No. I Signal
Green

4925

6-9

No. 2 Signal
Green

5100

19-4

Cobalt

4675

375

dbyGoogk

1 66 COLOUR MEASUREMENT AND MIXTURE.

The following are determinations of some
coloured pigments —

Coloured
Papers.

Wave-lengths

OF Dominant

Ray.

Percent-
age OF
White
Light.

Percentage
OF Lumin-
osity,
White
Paper

BEING 100.

Vermilion

6100

2*5

14-8

Emerald Green

5220

59*0

227

French Ultra- 1
marine Blue .

4720

6i-o

4-4

Brown Paper

5940

50-0

25-0

>9 >>

5870

67-0

19-5

Orange

5915

4-0

625

Chrome Yellow

583s

26*0

Blue Green

5005

42-5

14-8

Eosin Dye

{Sporting Times)

6400

72*0

447 '

Cobalt

4820

iS'S

M'S

dbyGoogk

CHAPTER XIV.

Complementary Colours — Complementary Pigment Colours
— Measurement of Complementary Colours.

We are now in a position to enter into the question
of complementary colours, which is one of supreme
interest to artists. A complementary colour, in its
strictest sense, may be described as the colour
which, combined with the colour whose complement
is required, makes up white. In this definition we
have three characteristics to take into account, viz.
hue and luminosity, and dilution with white light.
As an example of what we mean we refer to an
experiment which was made and described at page
125. It was said that if the violet slit was placed
in a certain position in the blue of the spectrum, it
was possible to move the green slit into a part of
the yellow, so that the two colours when mixed
together would form white. In that case the blue is
complementary to the yellow, and the yellow to the

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l68 COLOUR MEASUREMENT AND MIXTURE.

blue, so long as the intensities are those which make
up white light Again, if it requires the light coming
through the three slits to make up white light, be
it the white of the electric light or that of gaslight,
we can obtain the complementary colour of the light
issuing through any one of them by covering that
slit up. Thus suppose the slits to be in the normal
position the complementary colour of the red is a
green-blue, formed by the mixture of the violet and
green rays, the complementary colour of the green
. is a purple, formed by the mixture of the red and
the violet light, whilst the complementary colour of
the violet is greenish yellow, formed by the mixture
of the red and green rays. It will be evident that
as the intensities of the three rays respectively will
be different according as the white light matched is
the electric light or gaslight, the complementary
colours in the former will be different in hue and
intensity to those in the latter.

Another couple of striking experiments which the
writer devised to show these colours can be made
with the colour patch apparatus, and on the same
principle as that used for obtaining the intensity of
the rays reflected from pigments, and transmitted
through coloured transparent bodies. Instead of the
small slit with a right-angled prism in front to deflect
the beam from the top spectrum, where two spectra
a.re produced (see Fig. i6, p. 97), a single spectrum

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COLOUR MEASUREMENT AND MIXTURE. 1 69

is used, with a right-angled prism of such a size
that it deflects half of it, which is again reflected on
to the screen by a mirror, and through a lens to
form a second patch of equal size as the unde-
flected beam. A rod can be so placed in the path
of the beams that two coloured stripes are formed,

RED

Fig. 38.— Chromatic Circle.

together with a white stripe caused by their over-
lapping. The two coloured stripes are comple-
mentary one to the other. By moving the prism
along the spectrum various coloured stripes can be
formed, in some cases t)ne being much less luminous
than the other, and yet they are complementary.
If instead of the large right-angled prism a smaller
one be used, the complementary colour due to ^

dbyGoogk

I/O COLOUR MEASUREMENT AND MIXTURE.

small part of the spectrum can be shown in the
same manner.

It is customary to show the complementary
colours diagrammatically by what is known as the
chromatic circle. Roughly it is drawn as in the
above figure (Fig. 38). The three colours, red, green
and blue, which are taken for primary colours, are
placed at 120* apart in a circle, and lines drawn from
them through the centre, at which white is supposed
to be situated. Where these lines cut the circum-
ference is placed the complementary colour. Other
colours can be placed round the circle with their
complementary colours opposite, and so a fairly
complete diagram of the spectrum can be made.
But it must be remembered that this is really of
no scientific value, as it conveys no idea of the
luminosity of the spectrum colours, nor of the
quantities which have to be mixed together to form
the complementaries. Such a circle is, however,
convenient as a sort of memoria technical and can
be filled up according to the fancy of the observer.

The following are pairs of most carefully selected
complementary colours of pigments, as adopted by
Professor Church.

CompUmerUaries. Pigments,

i Red Madder red or crimson vermilion.

\ and

(Green blue Viridian, the emerald oxide of

ghromium with a little cobalt,

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COLOUR MEASUREMENT AND MIXTURE. 171
Complementaries, Pigments,

f Orange Cadmium yellow, of full orange

■< and hue.

( Greenish blue Cobalt green.

i Orange yellow Cadmium yellow, or deep chrome.
J and

(^Turquoise Coerulium, or cobalt blue, with a

little emerald green,

f Yellow Lemon yellow, pale chrome, or

< and aureolin.

(.Blue Ultramarine from lapis-lazuli.

f Greenish yellow Aureolin with a little viridian.

j and

(violet blue French ultramarine.

i Green yellow Lemon yellow, with some eme-
-< and raid green.

I. Violet French ultramarine with madder

carmine.

TYellowish green Lemon yellow with much eme-
-< and raid green.

(.Purplish violet Madder carmine with French
ultramarine.

r Green Emerald green with lemon yellow.

-J and

(.Purple Madder carmine with French

ultramarine.

J Emerald green Emerald green alone.
. and

( Reddish purple Madder carmine with a little
French ultramarine.

dbyGoogk

172 COLOUR MEASUREMENT AND MIXTURE.

As these pairs of pigments are complementary,
it follows that if rotated together in proper propor-
tions, they should make a grey which will be in-
distinguishable from a grey formed by rotating
black and white sectors together. (See chap. XV.)

It will probably happen that a good deal more of
one of the pairs of the colours is required in the disc
than of the other, and supposing that the two are
each used of the full brightness which the pigments
are capable of giving, it follows that in a diagram
where equal areas are filled with the pigments as
complementary, some means must be adopted to
give the true depth of tone to each. The mixture
of white will heighten the luminosity of either, or
the admixture of black will lower it, but often
alters the hue.

One of the most beautiful methods of observing
complementary colours is by means of the polariza-
tion of light, which we need not describe in detail
What is known as Briicke's schistoscope is perhaps
one of the most convenient. Dove*s Iceland spar
prism is also useful, when two pigments have to be
worked on to paper, so as to be complementary.
The two squares of pigmented paper are placed
side by side, and two images of each are formed.
One image of one colour can be caused to over-
lap the second of the other, and if the two when
superposed appear of a grey they are comple-

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COLOUR MEASUREMENT AND MIXTURE. I73

mentary one to the other. If too much of one
colour appears, it must be toned down till the grey
is formed. This is a very simple piece of apparatus,
and for experiments with pigments will be found to
be very handy. When the right tint of each is
secured in this manner, a further test may be made
by making the pigmented surfaces into sectors, and
rotating them together, when if the double-image
prism gives correct results, the angular aperture of
the sectors should be 180** each, to match a grey
produced by a mixture by rotation of black and
white.

We have klready shown how the complementaries
of the Spectrum colours can be found ; the question
is can we find the complementaries of pigments by
the spectrum ? There is one very self-evident way.
We can place the three slits in the spectrum as
given in chapter IX., and match in intensity the
white light of the reflected beam, and note the
apertures of the slits. We must then in the
reflected beam place the pigment whose comple-
mentary colour is required, and match its colour
with the light from the three slits, keeping, for
the sake of convenience, the white light falling on
the pigmented surface of unaltered intensity, and
again note the apertures. If we deduct the last
measures from the first, the difference of aperture
will give the complementary colour. Thus it was

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174 COLOUR MEASUREMENT AND MIXTURE.

found that with slits in a certain position in the
spectrum, to make white light the following aper-
tures in hundredths of a millimetre were required :

Red ... i6s

(i) - Green ... 60

Violet ... 100

Emerald green was placed in the patch ayd was
matched by the light from the three slits, when it
was found that it required

(2)

Red ... 4
Green ... 35
Violet ... 25

Deducting one from the other we get as the
complementary colour,

(3)

Red ... 125

Green ... 25
Violet ... 75

This is a complementary colour, but like the green
itself it is mixed with white light ; but we can
easily deduce what is the simplest complementary
colour ; for we have only to deduct the possible
white light from the second measure. Now evi-
dently the greatest amount of white light is when
the whole of the green is taken as forming part of
it, with the proper proportions of red and violet.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 1 75

and these we can obtain by taking the proportions
of the colours in (i) ; therefore deduct —

(Red ... 69
Green ... 25
Violet ... 41-5

and this would leave as the complementary colour
without any admixture of white —

rRed ... 56
^^^ 1 Violet ... 33-S

which is a purple as would be expected.

Now to give the same dilution of white to'^e
complementary that the emerald green has, we
must take away from the emerald green all the
white mixed with it, and add that quantity to
the complementary. The white in the emerald
green can be found by treating the whole of the
red as going to form the white ; we then have
from (i) —

Red ... 40
(6) - Green ... 14-4
• [Violet ... 24

Deducting these from (2), we find that the colour
of emerald green, less the white light, is 20'6 of
green mixed with i of violet. To find the proper
dilution of the complementary colour we must add
the above proportions of the three colours, and as

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1/6 COLOUR MEASUREMENT AND MIXTURE.

our final result we find the complementary colour,
of equal impurity, is a mixture of —

Red ... 96
(7) - Green ... 14*4
[violet ... 57-5

The slits may be set at these apertures and a colour
patch thrown on the screen, and we shall find it of
a delicate pink. The truth of this can be seen by
using a double-image prism to view the pigmented
surface, illuminated by the same white light as that
in which it was measured, and the colour patch
on the screen by its side. The two colours may
be caused to overlap, when it will be seen that
white is produced.

Another example was an orange pigment, and
this we will work out in the form of colour equation.
The same mixture gave white, viz.:

165 R + 60 G + 100 V =* W
165 R + 42 G - O

. • . the complementary colour, which is

W - O = 18 G + 100 V,

or a dark-blue colour. In this case there was
apparently no white light reflected from the orange.
It was slightly glossy, and as polarized light was
used for the reflected beam, it was probably some-
what quenched ; but what is more probable is that

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COLOUR MEASUR3EMENT AND MIXTURE. I//

the green contains some violet as well as red, for
the reasons given in chapter XI. The reason we
have been particular in showing to what extent
complementary colours must be diluted with white
to the same proportion that the colour itself is
diluted, will be apparent if considered for a
moment. A deep brown is in reality orange,
much degraded in tone, and can be produced as a
colour patch on the screen if a bright orange pigment
be placed in the reflected beam of the colour patch,
and the light nearly shut off by the rotating sectors.
Now the same complementary colour will be found
for both, but if we were to use the bright comple-
mentary colour which we obtained with the orange
for the brown, and endeavoured to obtain a white
with it by means of the double-image prism we
should fail, as the complementary colour would
predominate. Complementary colours can always
be formed by a mixture of only two rays, and
although the overlapping images may form white,
yet when the two are placed side by side, it often
will be found that the complementary, unless
diluted with white, is evidently too dark to be
satisfactory, but the luminosity may be increased
by adding white to it, as any amount of white may
be added to the mixture of the two rays which
form the complementary, and of course white will
still be formed with the original colour. It is thus

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178 COLOUR MEASUREMENT AND MIXTURE.

quite feasible to give the complementary the same
luminosity as the latter by adding white light to
it. Like the colour itself, the complementary
colour can always he expressed either by a single
ray of the spectrum, or by white light from which
a single ray is deducted. (See chapter XI 1 1.)

dbyGoogk

CHAPTER XV.

Persistence of Images on the Retina— The Use of Coloured
Discs.

By this time we must be thoroughly convinced
that by throwing one coloured patch over another a
compound colour can be formed ; our next business
is to demonstrate that the same effect can be pro-
duced by successive images of these same colours.
Thus we can show that as a mixture of red and
blue produces purple, when the two lights are
superposed, so precisely the same purple can be
produced by allowing the same two colours to strike
the eye alternately, and in very rapid succession.
We can make a match of the beautiful purple of per-
manganate of potash as before upon the screen, by
placing one adjustable slit in the red and the other
in the violet. If we place in front of the slits a disc
cut out with equal angular apertures (Fig. 39), the
slit Si will be covered when the slit Sa is open,

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l80 COLOUR MEASUREMENT AND MIXTURE.

and vice versdy and the two will never be uncovered
at the same time when the card is turning round its
centre. When this disc is caused to rotate rapidly,
we shall have first a patch formed by the light
coming through one slit, and then another formed
by that coming through the other slit, thrown on the

Fig. 39. — ^Disc to cause alternate opening and closing of two Slits.

screen on the same place in rapid succession, and
the effect on the eye should be precisely the same
as if the disc was not there, save in the matter of
intensity. Applying this artifice experimentally to
the two slits which were used to give the colour of
permanganate, the experiment tells us that such is
the case. It would be going away from the intention

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. l8l

of this work were the physiological aspect of this
experiment dwelt upon ; it need only be stated that
an impression on the retina lasts an appreciable
time, though short, and that the impression made
by the blue patch has not had time to disappear
before there is an impression made by the red
patch, and so on. As the retina retains these two
impressions together, they produce the impression
of purple.

For experiments in colour this duration of
impressions is of great value, for we can take
advantage of it to com-
pound the colours of
pigments together in a
very simple manner.
For instance, we can i
take a circular disc
painted in sectors with
blue and red (Fig. 40),
and produce a purple by
causing it to rotate round
its centre. Small discs
of two inches in diameter may be painted
with different coloured sectors, and if a pin be
passed through the centre, a smart movement
of a finger at the periphery will cause it to
rotate sufficiently quickly to make the colours
blend. A more convenient plan for exact work

Fig. 40. — Disc painted Blue and
Red.

dbyGoOgk

1 82 COLOUR MEASUREMENT AND MiXtURE.

IS, however, to have an electro-motor similar to
that which moves the rotating movable sectors

(Fig. 41), and at the end of the spindle to fix a cap
with a screw and nut attached. The disc, per-

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 1 83

forated at the centre with a clean-cut hole, can be
slipt over the screw, and fastened by the circular
nut. When the armature rotates, the disc also
rotates at the same speed, and the colours thus
blend without any exertion on the part of the
observer. Ordinary tops can also be used, but it
IS somewhat fatiguing to have to wind them up
and start them afresh for each experiment. The
motor shown in the figure rotates sufficiently
rapidly, with discs of eight inches in diameter, to
blend colours. It may here be remarked that the
stronger the light in which such sectors rotate, the
quicker the rotation should be. Too slow a rotation
allows a scintillation which is destructive of accu-
racy of reading. To blend some colours together
also requires more rapid rotation than with others.
The brighter the colour the more rapid it should be
We learn from this that the diminution of the more
intense impressions on the retina is more rapid at
first than of the feebler.

Very convenient discs for producing colours by
rotation of sectors may be made by the following :
vermilion (V), emerald green (E), French ultra-
marine blue (U), chrome yellow (Y), lamp-black
(X), and (zinc) white (W). With these nearly every
colour can be produced, or its value derived. The
chrome yellow disc is somewhat superfluous, but is
sometimes useful. The alteration in the proportions

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1 84 COLOUR MEASUREMENT AND MIXTURE.

of the colours can be readily made by Clark- Max-
well's plan. From the circumference to the centre
he cut the discs open, as at ab (Fig. 42). Any
moderate number of discs, similarly cut, may be
slipt over one another, and
only a sector of each is left
visible. It should be remarked
that this necessitates the rotat-
ing apparatus being viewed
with a direct light, as in the
case of two or three over-
lapping discs it is impossible ^ ^. ^ ^ ,

X ^ . . , « , Fig. 4a.— Method of cut-

to keep them entirely flat, and ting Disc to allow an

shades are apt to be introduced, overlap of a second Disc
If we wish to produce a white, or rather a grey,
from three colours, we can take three small discs
of V, E and U, of equal diameter, and behind
them place discs of black and white, of larger
diameter, rotating the whole five on a common
centre. We shall find that by altering the pro-
portions of the three first we can get a grey
which can be exactly matched by a mixture of
black and white, X and W. It has already
been shown that even lamp-black reflects a certain
amount of white light, so this amount of reflected
white light has to be added to the white in
the outside sectors. In the sectors used in the
following experiments it was found that the

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COLOUR MEASUREMENT AND MIXTURE. 18$

following proportions of the three colours were
required —

V = 124'

E = I43«

360^
and to make the same grey it required
X = 278°
W = 82'

360°
Now the black reflected 3*4% of white light, so
that really the proportions of black and white were

X = 268-6

W = 91-4

360-0
These matches were made in the light emitted by
the crater of the positive pole of the electric light,
and are correct only for this light. The greys here
are dark greys, and such greys can be matched
exactly by throwing the white light in which the
comparisons were made on a white card, and re-
ducing the intensity by means of the rotating sectors.
We can prove whether our matches are fairly cor-
rect from our previous measures of the luminosity
of these three colours, in comparison with that of
white. The luminosities of V, E, and U, as found

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186 COLOUR MEASUREMENT AND MIXTURE.

from the measures (pp. 93-95), are 36, 30, and 4*4,
white being 100; 124 of V would have a luminosity
of^^,or 12*4; 143 of E would have 11-92; and 93
of U would have 1*14 ; which, added to either, give
a luminosity of 25*46. The luminosity of ^ of
white, which is that of the mixture of black and
white, comes to 25*39, so that we may assume our
observations have been fairly correct.

The influence of the kind of light in which the
match was made is well exemplified by taking the
matched discs whilst rotating into a room illumin-
ated by the light from the sky, when it is seen
that the grey of the outer discs is bluish ; or again,
if the matched discs be examined in gaslight, the
inner grey will be found too blue.

The match of grey in this last light was found
to be

V = 119*'

E = 148'

U - 93^

360**
which matched with

X = 244^
W = ii6«

(In this case the black and white are the corrected
black and white.)
The importance of making matches in a uniform

dbyGoogk

COLOWR MEASDRfiMENt AND MiXtURE. 1 87

light is fairly demonstrated by this experiment, and
we cannot be wrong in asserting that as skylight
and sunlight and cloudlight (the last being often
a mixture of the two first), are so variable no
measures made on one day can be fairly compared
with those made on another, more especially if
the observers are different. With an emerald green,
a vermilion, an ultramarine, a white, and a black
disc any colour may be reproduced in the rotation
apparatus, the three first nearly matching what we
have already stated to be the three primary colours.
It may seem curious that both black and white
may have to be mixed with the colours, to pro-
duce a pigment colour ; but a little reflection will
show how it is. For instance, suppose we want to
know the colour composition of gamboge (Y) in
terms of vermilion (V), emerald green (E), and
ultramarine blue (U). We must make a disc
painted with gamboge, and also a black and a
white disc of the same diameter, but rather larger
than the other three discs, and place them on the
spindle of the electro-motor (Fig. 43). We shall
soon see on rotating them that no blue is required
in the inner disc, and that all that remains to do
is to use the red and the green. Mix these two,
however, in whatever proportions we may, the
mixture will never attain the same luminosity,
consequently we -must darken the yellow with

dbyGoogk

188 COLOUR MEASUREMENt AND MIXTURE.

black. Even then we shall find that, add what
black we may, the rotating red and green sectors
will always be a little less saturated with colour ;
which means that on rotation they produce a
certain quantity of white light mixed with the
yellow. This we might expect, for as emerald
green, besides green and red, also contains a fair

Fig. 43. — Arrangement to find value of Gamboge in terms of
Emerald Green and Vermilion.

proportion of blue, and as red, green and blue
when mixed give white, it follows that when V and
E are rotated together, a grey or subdued white
light must be mixed with the colour produced.
Turning back to Chapter XIII. we also see that as
the emerald green is expressible by a single ray of
the spectrum, mixed with white light this result
might have been foretold.

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. 189

This necessitates adding some white to the rotat-
ing sectors of the yellow and black, as the yellow
reflects but little white light, and finally we shall
get an absolute match, of which the final results
are

172 V+ 188E = 7SY + 4SW + 24oX.

This equation is full of meaning. It tells us in
the first place what we have already known, that V
and E are one or both impure colours, and that when
rotated together in the proportions indicated, they
produce at least a luminosity of white equal to ^ of
a white disc (as the black used reflected just 3'4Vo of
white light). Further, it tells us that we can obtain
the luminosity of Y, when we know the luminosities
of V and E. At page 186, the luminosities of these
colours are given as 36 and 30 respectively, white
being 100. This makes the luminosity of the
colours on the left hand of the equation 17-2+1 5*67,
or 32*87, and on the right -^ Y + 1476, and con-
sequently the luminosity of Y = 869. In the
same way we can obtain any other colour in terms
of these standards.

We may here show how we can obtain the
luminosity of any colour by means of the three
inner discs, and the black and white outer discs.
We have already shown that any colour may be ^
matched by the combination of not more than two
simple colours, after deducting white from it ; and

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igO COLOUR MEASUREMENT AND MIXTURE.

from this we deduce that any coloured pigment
will form a grey with some two of the three
coloured discs, V, E, and U ; and this being done
we can then calculate the luminosity. For in-
stance, with an orange-coloured pigment we should
proceed to make a disc of the same diameter
as that of the three above ; an inspection would
show us that in this colour red predominates, and
therefore we could do without the red disc. We
should then alter the proportions of V, U, and O,
till they gave a match which was the same as that
of a grey given by the rotating black and white
sectors.

In an experiment with an orange of this kind,
the following results were obtained —

u i;':) . r *'•

O 9S-i 'X ^75-

We can now from these deduce the luminosity
of the orange employed in this case.

The luminosities of E and U, as already found,
were 30 and 44, whilst the black (X) reflected
3*47o of white light; we thus get the following
equations —

115x30+150x4-4 + 95 = (85 + 3-4x275) 100.

This gives 95 O = 943S-(3450 + 660).

O = 56.

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E 35)
U204 = {
Y 121) ^

COLOUR MEASUREMENT AND MIXTURE. I9I

That IS, the luminosity of the orange is '56 that
of white ; by direct measurement it was -57.

In a similar way the luminosity of chrome yellow
(Y) is found. In this case —

^ -^ ' W loi

X 259

Similar equations were formed as the above.
35 X 30 + 204x4-4+ 121 Y =(101+3-4x259) 100
whence Y = yy'6.

That is, the luminosity of the chrome yellow is
•78 ; the same as was obtained by direct measure-
ment.

In the same manner the luminosity of any colour
can be found. Thus that of a purple, or of green,
can be ascertained ; of the former by using the
green disc with either the red or the blue disc, and
the latter by the red and blue disc. From this it is
apparent that we can check the luminosities derived
from other means by this plan.

A taking experiment can be made with colour
discs to imitate all the colours of the spectrum in
their proper order, though diluted more or less by
white light. This can be done by rotating V, E, and
U together; but in order to get additional luminosity
in the yellow, we can use chrome yellow as well.
If a disc be made as in the figure (Fig. 44), it will on
rotating give a fair imitation of the spectrum, if it
be viewed through a slit held in front of the disc.

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192 COLOUR MEASUREMENT AND MIXTURE.

The mixture of colours by means of rotating
sectors is one which the artist cannot use for artistic
purposes, and it might seem that for him any
deductions made from this method are useless ; but
it is not so. Suppose we take black lines ruled
closely together on paper, and examine the surface

Fig. 44.— Disc arranged to give approximate^ all the Spectrum
Colours.

from such a distance that the lines are no longer
distinguishable it will appear of a grey ; and if we
take the amount of black on the paper and amount
of white, and prepare two sectors of black and
white, whose angles are in these proportions, and
rotate them alongside the ruled surface, it will be

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COLOUR MEASUREMENT AND MIXTURE. I93

found that the grey of one matches the grey 6f the
other. If instead of lines of black and white we
have them of light yellow and cobalt blue, a grey is
also produced when the surface covered by the
blue is to that covered by the yellow in correct
proportions, and may be matched by rotating
sectors containing merely black and white. Now
some artists employ stippling, filling up cross-
hatching of one colour with dots of a totally
different colour, or they place dots side by side.
When seen from the distance at which the picture
should be viewed, these various colours blend one
into another, and form a tint which is the same
as that which would be obtained by rotating these
colours together in the proportion in which they
cover the ground. Artists, however, generally mix
their pigments together on the palette, and the
resulting mixtures are often totally unlike those
which are obtained by rotating the same colours
together, a noteworthy example is that of yellow
and blue. By rotation, and when in proper pro-
portion, these two give a white, but when mixed
on the palette a green results. What causes this
diflference ? Experimental proof is always the
most satisfactory proof, so let us have recourse
to the spectrum apparatus to obtain an answer,
Let a spectrum be thrown on the screen, and in
it place a strip of paper painted with the yellow,

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194 COLOUR MEASUREMENT AND MIXTURE.

and then another with the blue. With the first it
will be seen that the blue rays are not reflected,
but only the green and yellow and red, taking the
spectrum as roughly made up of these four colours.
With the latter the yellow is not reflected, and
but very little red, but the blue and the green are
reflected strongly. Now we have already said that
the reflection of colour from a surface is indicative
of the colours the particles of pigments when taken
thin enough to be transparent would transact ;
hence we may take it that the yellow pigjment
transmits the red, yellow, and green, and the blue
pigment scarcely anything but blue and green.
When we have a mixture of these fine particles
of pigment on paper, some will underlie the others.
But let us pay attention to what would happen if a
yellow particle were at the top, and a blue one
beneath it. White light would impinge on the yellow
particle, but only red, yellow, and green would pass
out or be reflected from it. This sifted light would
next fall on the blue particle and — as we have
seen— only blue and green can pass through or
be reflected from it ; but as the yellow particle has
already deprived the white light of its blue com-
ponent, the green light alone would pass to the
paper, and be reflected either direct from the surface
of the paper, or through the particles themselves
to the eye. If the blue particle were on the top,

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. IQS

precisely the same effect would be produced ; it
would only allow blue and green to pass to the
yellow particle, and as the yellow is opaque to the
blue, only green light again would pass. Similarly
if side by side the same phenomena would occur,
since the light reflected from one on to the other
would be deprived of all colour except the green.
A very pretty experimental proof of this is to place
a yellow solution of dye in front of the slit of the
colour apparatus, and having formed the yellow
colour patch to place in it a piece of paper covered
with a blue pigment : the latter becomes green. By
placing a blue solution in front of the slit, and using
a piece of yellow pigmented paper, the same result
is obtained. The artist therefore in mixing his
pigments calls into play the law of absorption, and
from his mixtures very naturally assumes that blue
and yellow make green. He makes a neutral tint
of blue, red, and yellow, and as the red cuts off the
green, this naturally follows from the above. Such
experiments as these led him to the conclusion that
red, yellow, and blue are the three primary colours,
an assumption which had he used simple spectrum
colours instead of compound colours, such as pig-
ments, he would not have ventured to make.

dbyGoogk

CHAPTER XVI.

Contrast Colours — Measurement of Contrast Colours —
Fatigue of the Eye — After-images.

There is a phenomenon in colour which must be
alluded to, and which possesses more than a passing
interest to the art world, and that is colour contrast.
Perhaps one of the best methods of showing this is
by our colour patch apparatus. If we throw the
reflected beam and the colour
patch on a square as before,
and place a rather thinner
rod in front, so that the two
shadows lie on a background
of the combined white light
and spectral colours, on pass-
ing a slit through the spec-
trum, the shadow which is
illuminated by white light will appear anything
but white. Thus if we allow yellow spectral light
to illuminate one shadow, the other will appear

Fig. 45.— Method of show-
ing Contrast Colours.

dbyGoOgk

COLOUR MEASUREMENT AND MIXTURE. I97

decidedly of a blue hue ; if a green ray it will be of
a ruddy hue ; if a blue ray of a yellow hue; that is,
all the contrast hues will appear to the eye to tend
towards a complementary tone to the spectral light.
The kind of white light illuminating the shadow has
a marked effect on the tone, as might be expected.
The following table shows the contrast colour of the
white illuminated shadow when the white light used
was that of a candle.

Spectrum
Colour.

Contrast

Colours in

Electric light.

Spectrum
Colour.

Contrast
Colours im
Gaslight.

Cherry red

Green gray

Cherry red

Green gray

Scarlet

Bluish green

Scarlet

Sap green

Terra cotta

gray
Blue gray

Light red

Green gray

Raw sienna

Light blue gray

Olive green

Pink gray

Olive green
Emerald green

Umber

Apple green
Emerald green

Mauve & black

Pinkish laven-

der
Light pink

Pinkterra-cotta

Grass green

Emerald green

Pinkterra-cotta

Bluish green

Dark pink

Bluish green

Pinker terra-
cotta

Signal green

Salmon

Peacock blue

Salmon

Cyanine blue

Yellow ochre

Prussian blue

Reddish yellow

Ultramarine

Raw sienna

Ultramarine

Raw sienna

Violet blue

Brownish yel-

Violet blue

Brownish

low

orange

Blue violet

Green yellow

Blue violet

Brownish

brown

yellow

Violet

Burnt sienna

Violet

Yellow ochre

The contrasts here shown are not so visible when
the two shadows of the rod occupy the whole of

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198 COLOUR MEASUREMENT AND MIXTURE.

the whfte square, but are decidedly increased by the
shadows occupying only a part of the field, the
margins being illuminated with a mixture of the
two lights. Not only are there contrasts with
coloured light and white, but the relative position
of one colour to another may alter the hue of
each to the eye. The following experiments in-
dicate what change can be expected in contrasted
colours. The double colour apparatus was used as
described at page 122, and a slit was placed in four
different positions in the spectrum, viz. in the red,
orange, green, and violet, to form patches, and
another slit was placed in the same four positions
in the other spectrum, and the contrasts noted.

Origixal Colours.

Change due to Coxtrast.

Red

99
99

Green

Orange
Violet

Orange

Green

Blue

Violet

Orange

Blue

Violet

Blue

Violet

Blue

Red became yellower

„ unaltered, but

brighter
„ became more

orange
„ became orange

Green became bluer

„ became olive

„ became yel-
lower
Orangebecame redder

„ became greener
Hardly altered

Orange became green

grey
Green unaltered, but

brighter
Blue became greener

Violet, no marked
change

Orange became yel-
lower

Blue became more
violet

Violet became bluer

Blue became bluer
Violet became bluer
Hardly altered

dbyGoogk

COLOUR MEASUREMENT AND MIXTURE. I99

These contrasts were in most cases very marked,
as would be seen by causing the same colours to
fall on a different part of the screen, outside that
on which the comparisons were made.

This phenomenon of contrast is one which is most
valuable for artistic purposes, for it gives a power
of increasing the value of the colour of pigments
which is used by the artist almost intuitively. Thus
he can heighten the tone of his orange pigment,
with which he makes a sunset sky, by placing in
juxtaposition with it some bit of blue coloured space.
The blue becomes bluer, and the orange more
orange, by this artifice. All these artifices — or
rather we should say intuitive applications of science
— are most necessary when the small range of
luminosity of colours with which he has to deal is
taken into account. For instance, in a picture of a
sun-lighted snow mountain and deep pine forests,
the utmost luminosity he can give to the former is
that of white paper when seen in the shade, which,
in comparison with what he sees, is really a mixture
of 90% of black with the light from the snow, so
that his range of luminosity is only nine-tenths of
that which occurs in nature. It is in adapting this
low scale to his picture that true genius of the
artist is seen.

It might seem that these contrast colours being
only a physiological effect, could not be accurately

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20D COLOUR MEASUREMENT ANJD MtXTORft.

measured, but such is not the case, if a little arti-
fice be employed. If we use the second colour
patch apparatus side by side with the first, we can
very readily and with very close approximation
determine the contrast colours we see. Suppose by
the second apparatus we form a colour patch of say
red, and place a thin rod in the beam of this ray
and of the reflected beam, and about six inches
from it form another patch with the first apparatus,
using the three slits to make colour mixtures ; by
first noting the contrast colour, and then approxi-
mating in the second patch to what the eye perceives,
we can little by little get a fairly exact match to the
contrast colour, and can definitely note it. We now
give the results of three measures made for the con-
trast colours which presented themselves to the eye
when they were caused by a red ray near the
lithium line, another near the E line in the green,
and the third near the G line in the violet.

To make white light and the contrast colours, the
slits had to be of the following apertures —

Colour.

Red.

Green.

Violet.

White light

Contrast to Red
„ Green
„ Violet

157
13-5
15-8
15-9

6S
n-8

7-2

9-8

22-5

4-8
4-2

Thus to form the contrast to red took I3'S of red,

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COLOUR MEASUREMENT AND MIXTURE. 201

1 1 "8 of green, and 22*5 of violet. Now from each of
these there can be deducted the amount of white
light, which will leave only two colours mixed.
Calculating this out we find that the contrasts
are —

Contrast Colour

Red.

Green.

Violet.

Red

Green

Violet

157
19-4

3'S
32
9*5

167

If the contrasts were exactly complementary
colours, the proportions of the two colours left
should be the same as those of the same colours as
given, which with the original colour make white
light. It will be seen that such is not the case.
A very simple way of testing this is to form a
patch of white light with the three slits in the first
apparatus, and then to obtain the contrasts by the
other apparatus, with the same colours one after
the other that pass through the three slits. If
now we cover up the slit in the first apparatus
through which the colour whose contrast in the
second apparatus is sought passes, we may dilute
it with white light as we will, but in no case has
the writer found that an exact match to the con-
trast colour can be obtained in this way. Thus,
supposing we wanted to try the experiment with

dbyGoogk

202 COLOUR MEASUREMENT AND MIXTURE.

the same red light as that which comes through
the red slit, we should use that same light in the
second apparatus, and form the contrast colour
with the white beam, and then in the first apparatus
cover up the red slit, leaving the violet and green to
form a patch on the screen. We should then dilute
the colour of this patch with white light, and note
if it appeared the same as the contrast colour.

Another phenomenon which presents itself is the
fatigue of the colour-sensation apparatus of the
eye, induced by looking at a bright object. For
instance, if we look at a crimson wafer or spot for
some time, and then turn the eye so that it rests
on a grey surface, an image of the spot will still
be seen, but as of a greenish-blue colour. This
is due to the fact that the red-seeing apparatus is
fatigued and exhausted, whilst the green and violet-
seeing machinery has not been largely exercised.
Consequently when looking at grey paper the grey
of the paper is seen in the retina at all parts as grey,
except in the small part of the retina which has got
diminished power of perceiving a red sensation ;
hence a sea-green image will be seen until the
fatigue has passed away. This colour can be repro-
duced with very fair accuracy by allowing only
one eye to be fatigued, and then using the other
to obtain a colour mixture corresponding to it* It
will then be found that the colour is the same as

Digitized by LjOOQ IC

COLOUR MEASUREMENT AND MIXTURE. 203

the complementary colour, much diluted with white
light.

To the same cause may be traced positive and
negative after-images, as they are called. If we
look at a strongly-illuminated coloured form, such
as a church window, and close the eyes, the window
will still be seen, at first of its original colour (a
positive after-image), and it will then fade and be
seen in its complementary colours (a negative after-
image). The positive image is due to the persist-
ence of what we may call nerve irritation, whilst
the negative image is due to the physiological
excitation of all the nerve fibriles, which ordinarily
speaking give the sensation of a very dull white
light The previous fatigue of one set of fibriles,
however, prevents them being excited to the same
degree as the others, hence we get a comple-
mentary image. It would be out of place to
pursue this subject further, as we have only dealt
with the physical measurement of colour-sensations,
and these are beyond it.

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INDEX.

Absorption by red, blue, and

green glasses, 53
Absorption of light in the earth s

atmosphere, 67
Absorption, reference to law of,

After-glow, 74

Arc light, 20

Artists and colours, 195

Balmain's paint, 33
Black body, 18
Blindness to green, 142
Blindness to red, 79-142
Bromo-iodide of silver, 136

Carbon poles, 20

Carmine, light reflected from, 107

,, template, 106
Chlorophyll, green solution of, 51
Collimating lens, focal length of,

22
Colour, analysis of, 52
Colour-blind, red and green, 79, 80
Colour-blindness, 142-146, 157,

159

Colour constants, 15

Colour eouationsi formation of,

147, 148 . .
Colour, extinction of, by white

light, 126

Colour mixtures, 113
Colour patch apparatus, 41-52
Colour sensation of the eye, 202
Coloured discs, use of, 189
Coloured glasses, measurement of,

162
Colours, complementary of pig-
ments, 170-172
Colours, complementary of spec-
trum, 167
Colours, how matched, 156, 157
Complementary colours, measure-
ment of, 173-178
Compound colours, definition of,

16
Continuous spectrum, 17
Contrast colours, 196-200

Diffraction gratings, 23
,, spectra, 24
Dimness and brightness of spec-

trumj 29
Discs, spinning, 182
Dust, particles of, 62

Electric light, contrast colours in,

197
Electric light, crater of positive

pole of, 20
Emerald green, light reflected

from 94,

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206

INDEX.

Equations, colour, 147
Enentials of spectrum, 22
Eztrmctioii of colour by white

light, 126
Extraction of white light by

colour, 131
Eye, sensitiveness of, 15

Fatigue of the retina, 202
Fluorescence, 31
Fundamental sensations, 140

Gambo^ matching, 189
Glass, li^ht from sheet of, 14
Glass pnsms, 21, 22
Glow-worm, 13
Green colour-blindness, 142

Heating effect of radiation, 38
Hue, 15

Images, after, 202

Images, persistence of, on retina,

179
Impurity of simple colours, 124
Indicator of sectors, 48
Infra-red ra3rs, 32

„ photography with, 34
Insensitiveness of the yellow spot

to green, 118
Intensities of limelight, gaslight,

and blue sky compared, no,

121
Interference, 58, 59
Interference bands on soap film,

60
Invisible spectrum, methods for

showing existence of, 32, 33

Kcenig*s curves, 151
Kcenig's experiments, 140

Law of the scattering by fine
particles, 66

Light from sun, imitation of, 63

Light, quality of, illumining
object, 14

Light scattered, 62

Limelight, 19

Lines m solar spectrum, 26

Luminosity, 13

Luminosity, addition of one to
another, 85-87

Luminosity of colour, 16

Luminosity of pigments, methods
of determining, 81, 82

Luminosity of spectrum to normal-
eyed and colour-blind persons,
76-78

Luminosity of sun at different
altitudes, 69-71

Maxwell's colour-box, 152, 153
Maxweirs discs, 184-186
Measurement of amount of light

reflected by different pigments,

88.92
Metals, light reflected from, 100
Mock suns, cause of change of

colour in, 64
Molecular physics, 54
Molecular swings, 136, 137
Monochromatic light, 47

Negative images, 203
Normal vision, 77

Orange, finding luminosity of, 190

Percentages of skylight, sunlight,

and gaslight, no, in
Phosphorescence, 32, 56
Pigments, absorption by, 57, 58
Plan of forming spectrum, 21
Polished and uneven surfaces, 15
Primary colours, definition of,

^ 133-135

Pnsm, Iceland spar, 96

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Prismatic spectrum into wave-
lengths, conversion of, 28

Prisms, drawback to use of, 23

Prussian blue template, 107

„ „ light reflected

from, 107

Purity of colour, 16

Kays, infra-red, 34
Kays, photography of dark, 34
Kays, ultra-violet, 34
Kegistering tint of pigments, 1 16

„ „ colours, 156

Ketina, persistence of images on,

179
Ritter's rays, 32
Kood's colour scale, 26
Rotating sectors, 46

Scaling of spectrum, 49

Sectors, rotating, 46

Simple colours, how obtained,

112,113
Slits placed in spectrum, 113
Soap-bubbles, 58, 59
Soap-films, 59

Spectrum, absorption of, 51, 52
Spectrum of sunlight, 18
Sun, mock, 64
Sunset clouds, 68, 69, 72, 73
Sunset sky, 72, 73

Thermopile, heating effects of, 36

INDEX. 207

Thermopile, principle of, 35
Vermilion, light reflected from,

y^l

•rations of rays per second, 55
Violet bands, brightness of, 21
Visible and invisible parts of
spectrum, 30

Ultramarine, light reflected from,

95
Ultra-violet rays, 31

Water, particles of, 62
Wave-length of lines in solar

spectrum, 26
White light and contrast colours,

200-202
White light, extinction of by

colour, 131
White light, formation of by

mixture of yellow and blue,

125
White light, how made, 114,115,

1 19-123
White light, impression of, 81

Yellow and blue make white, 125
Yellow, chrome, luminosity of.

Yellow n>ot, 117
Young-Helmholtz

THE END.

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